Hyperbolic Groups
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Hyperbolic spaces provably model tree-like structures better than Euclidean geometry.
“Following prior work, we first advocate for using hyperbolic spaces which provably model tree-like structures better than Euclidean geometry.”
From Hyperbolic Entailment Cones for Learning Hierarchical Embeddings (2018) · cites this paper as Gromov, 1987
Euclidean space R^n for n ≥ 2 is not δ-hyperbolic for any δ ≥ 0, while the Poincaré ball D^n is log(1+√2)-hyperbolic.
“For instance, the Euclidean space R n for n ≥ 2 is not δ -hyperbolic for any δ ≥ 0 , while the Poincar´ e ball D n is log(1+ √ 2) -hyperbolic.”
From Hyperbolic Entailment Cones for Learning Hierarchical Embeddings (2018) · cites this paper as Gromov, 1987
For any δ > 0, any δ-hyperbolic metric space and any set of points, there exists a finite weighted tree and an embedding f such that for all i, j, a distance condition holds.
“Theorem : For any δ > 0 , any δ -hyperbolic metric space ( X,d X ) and any set of points x 1 , ..., x n ∈ X , there exists a finite weighted tree ( T, d T ) and an embedding f : T → X such that for all i, j ,”
From Hyperbolic Entailment Cones for Learning Hierarchical Embeddings (2018) · cites this paper as Gromov, 1987
The exponential growth property enables hyperbolic spaces to embed any weighted tree while almost preserving their metric.
“This exponential growth property enables hyperbolic spaces to embed any weighted tree while almost preserving their metric 3 (Gromov, 1987; Bowditch, 2006; Sarkar, 2011).”
From Hyperbolic Entailment Cones for Learning Hierarchical Embeddings (2018) · cites this paper as Gromov, 1987
Cites
Lyndon, R. C., & Schupp, P. E. (2001) · Classics in mathematics · doi:10.1007/978-3-642-61896-3 · Cited by 1,026 · see citing works
Gromov, M. (1983) · Journal of Differential Geometry · doi:10.4310/jdg/1214509283 · Cited by 946 · see citing works
Self-citationFree subgroups in linear groups
Tits, J. (1972) · Journal of Algebra · doi:10.1016/0021-8693(72)90058-0 · Cited by 825 · see citing works
Manifolds of Nonpositive Curvature
Ballmann, W., Gromov, M., & Schroeder, V. (1985) · Progress in mathematics · doi:10.1007/978-1-4684-9159-3 · Cited by 784 · see citing works
Self-citationKlingenberg, W. (1978) · Grundlehren der mathematischen Wissenschaften · doi:10.1007/978-3-642-61881-9 · Cited by 500 · see citing works
Markov Partitions for Axiom A Diffeomorphisms
Bowen, R. (1970) · American Journal of Mathematics · doi:10.2307/2373370 · Cited by 484 · see citing works
Geometry and Topology of Manifolds
Boden, H. U., Hambleton, I., Nicas, A., & Park, B. (2005) · American Mathematical Society eBooks · doi:10.1090/fic/047 · Cited by 417 · see citing works
Valuations, Trees, and Degenerations of Hyperbolic Structures, I
Morgan, J. W., & Shalen, P. B. (1984) · Annals of Mathematics · doi:10.2307/1971082 · Cited by 340 · see citing works
Groups Generated by reflections and aspherical manifolds not covered by Euclidean space
Davis, M. W. (1983) · Annals of Mathematics · doi:10.2307/2007079 · Cited by 337 · see citing works
On the existence and irreducibility of certain series of representations
Kostant, B. (1969) · Bulletin of the American Mathematical Society · doi:10.1090/s0002-9904-1969-12235-4 · Cited by 271 · see citing works
L2-Cohomology and group cohomology
Cheeger, J., & Gromov, M. (1986) · Topology · doi:10.1016/0040-9383(86)90039-x · Cited by 249 · see citing works
Self-citationThe combinatorial structure of cocompact discrete hyperbolic groups
Cannon, J. (1984) · Geometriae Dedicata · doi:10.1007/bf00146825 · Cited by 247 · see citing works
A Fundamental Class of Geodesics on any Closed Surface of Genus Greater Than One
Morse, H. M. (1924) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-1924-1501263-9 · Cited by 217 · see citing works
Axiom A Diffeomorphisms have Rational Zeta Functions
Manning, A. (1971) · Bulletin of the London Mathematical Society · doi:10.1112/blms/3.2.215 · Cited by 199 · see citing works
Boundary theory and stochastic processes on homogeneous spaces
Furstenberg, H. (1973) · Proceedings of symposia in pure mathematics · doi:10.1090/pspum/026/0352328 · Cited by 180 · see citing works
Discrete Quasiconformal Groups I
Gehring, F. W., & Martin, G. J. (1987) · Proceedings of the London Mathematical Society · doi:10.1093/plms/s3-55_2.331 · Cited by 141 · see citing works
Finitely presented dynamical systems
Fried, D. (1987) · Ergodic Theory and Dynamical Systems · doi:10.1017/s014338570000417x · Cited by 102 · see citing works
Hyperbolic manifolds according to Thurston and Jørgensen
Gromov, M. (2006) · Springer eBooks · doi:10.1007/bfb0089927 · Cited by 100 · see citing works
Self-citationGroup Presentation, p-Adic Analytic Groups and Lattices in SL 2 ( C )
Lubotzky, A. (1983) · Annals of Mathematics · doi:10.2307/2006956 · Cited by 64 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Zomorodian, A., & Carlsson, G. (2005) · Discrete & Computational Geometry · doi:10.1007/s00454-004-1146-y · Cited by 1,591 · see citing works
Convex polytopes, Coxeter orbifolds and torus actions
Davis, M. W., & Januszkiewicz, T. (1991) · Duke Mathematical Journal · doi:10.1215/s0012-7094-91-06217-4 · Cited by 646 · see citing works
Carnot-Carathéodory spaces seen from within
Gromov, M. (1996) · Birkhäuser Basel eBooks · doi:10.1007/978-3-0348-9210-0_2 · Cited by 638 · see citing works
Self-citationGeometry of the Space of Phylogenetic Trees
Billera, L. J., Holmes, S., & Vogtmann, K. (2001) · Advances in Applied Mathematics · doi:10.1006/aama.2001.0759 · Cited by 575 · see citing works
Coverage in sensor networks via persistent homology
de Silva, V., & Ghrist, R. (2007) · Algebraic & Geometric Topology · doi:10.2140/agt.2007.7.339 · Cited by 422 · see citing works
Bowditch, Β. H. (2011) · International Journal of Algebra and Computation · doi:10.1142/s0218196712500166 · Cited by 389 · see citing works
Ripser: efficient computation of Vietoris–Rips persistence barcodes
Bauer, U. (2021) · Journal of Applied and Computational Topology · doi:10.1007/s41468-021-00071-5 · Cited by 383 · see citing works
Cyclic cohomology, the Novikov conjecture and hyperbolic groups
Alain Connes, A., & Moscovici, H. (1990) · Topology · doi:10.1016/0040-9383(90)90003-3 · Cited by 351 · see citing works
A combination theorem for negatively curved groups
Bestvina, M., & Feighn, M. (1992) · Journal of Differential Geometry · doi:10.4310/jdg/1214447806 · Cited by 301 · see citing works
Tree-graded spaces and asymptotic cones of groups
Druţu, C., & Sapir, M. (2005) · Topology · doi:10.1016/j.top.2005.03.003 · Cited by 300 · see citing works
Proceedings of the 19th Python in Science Conference
(2020) · Proceedings of the Python in Science Conferences · doi:10.25080/majora-342d178e-02b · Cited by 284 · see citing works
Acylindrically hyperbolic groups
Osin, D. (2015) · Transactions of the American Mathematical Society · doi:10.1090/tran/6343 · Cited by 276 · see citing works
The Theory of Multidimensional Persistence
Carlsson, G., & Zomorodian, A. (2009) · Discrete & Computational Geometry · doi:10.1007/s00454-009-9176-0 · Cited by 270 · see citing works
Zomorodian, A., & Carlsson, G. (2004) · Proceedings of the twentieth annual symposium on Computational geometry · doi:10.1145/997817.997870 · Cited by 264 · see citing works
Bounded cohomology of subgroups of mapping class groups
Bestvina, M., & Fujiwara, K. (2002) · Geometry & Topology · doi:10.2140/gt.2002.6.69 · Cited by 261 · see citing works
Kähler hyperbolicity and $L_2$-Hodge theory
Gromov, M. L. (1991) · Journal of Differential Geometry · doi:10.4310/jdg/1214446039 · Cited by 250 · see citing works
Self-citationAnosov representations: domains of discontinuity and applications
Guichard, O., & Wienhard, A. (2012) · Inventiones mathematicae · doi:10.1007/s00222-012-0382-7 · Cited by 247 · see citing works
An introduction to right-angled Artin groups
Charney, R. M. (2007) · Geometriae Dedicata · doi:10.1007/s10711-007-9148-6 · Cited by 240 · see citing works
Embeddings of Gromov Hyperbolic Spaces
Bonk, M., & Schramm, O. (2011) · Springer eBooks · doi:10.1007/978-1-4419-9675-6_10 · Cited by 238 · see citing works
Relative hyperbolicity and relative quasiconvexity for countable groups
Hruska, G. C. (2010) · Algebraic & Geometric Topology · doi:10.2140/agt.2010.10.1807 · Cited by 223 · see citing works
Cut points and canonical splittings of hyperbolic groups
Bowditch, B. H. (1998) · Acta Mathematica · doi:10.1007/bf02392898 · Cited by 220 · see citing works
Boguñá, M., Bonamassa, I., Domenico, M. D., Havlin, S., Krioukov, D., & Serrano, M. Á. (2021) · Nature Reviews Physics · doi:10.1038/s42254-020-00264-4 · Cited by 218 · see citing works
Hyperbolic Deep Neural Networks: A Survey
Peng, W., Varanka, T., Mostafa, A., Shi, H., & Zhao, G. (2021) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2021.3136921 · Cited by 220 · see citing works
Combination of convergence groupsPreprint
Dahmani, F. (2003) · Cited by 209 · see citing works
Ginestra Bianconi, A. (2021) · Cambridge University Press eBooks · doi:10.1017/9781108770996 · Cited by 207 · see citing works
Graphs of Some CAT(0) Complexes
Chepoi, V. D. (2000) · Advances in Applied Mathematics · doi:10.1006/aama.1999.0677 · Cited by 206 · see citing works
Fast construction of the Vietoris-Rips complex
Zomorodian, A. J. (2010) · Computers & Graphics · doi:10.1016/j.cag.2010.03.007 · Cited by 204 · see citing works
Constructing group actions on quasi-trees and applications to mapping class groups
Bestvina, M., Bromberg, K., & Fujiwara, K. (2014) · Publications mathématiques de l IHÉS · doi:10.1007/s10240-014-0067-4 · Cited by 201 · see citing works
Coordinate-free Coverage in Sensor Networks with Controlled Boundaries via Homology
de Silva, V., & Ghrist, R. (2006) · The International Journal of Robotics Research · doi:10.1177/0278364906072252 · Cited by 198 · see citing works
Generic-case complexity, decision problems in group theory, and random walks
Kapovich, I., Myasnikov, A., Schupp, P. E., & Shpilrain, V. (2003) · Journal of Algebra · doi:10.1016/s0021-8693(03)00167-4 · Cited by 176 · see citing works
Asymptotic geometry of the mapping class group and Teichmüller space
Behrstock, J. (2006) · Geometry & Topology · doi:10.2140/gt.2006.10.1523 · Cited by 174 · see citing works
Gromov, M. (2010) · Birkhäuser Basel eBooks · doi:10.1007/978-3-0346-0422-2_5 · Cited by 174 · see citing works
Self-citationThe classification of Kleinian surface groups, I: models and bounds
Minsky, Y. N. (2010) · Annals of Mathematics · doi:10.4007/annals.2010.171.1 · Cited by 173 · see citing works
The Borel Conjecture for hyperbolic and CAT(0)-groups
Bartels, A., & Lück, W. (2012) · Annals of Mathematics · doi:10.4007/annals.2012.175.2.5 · Cited by 170 · see citing works
Dehn filling in relatively hyperbolic groups
Groves, D., & Manning, J. F. (2008) · Israel Journal of Mathematics · doi:10.1007/s11856-008-1070-6 · Cited by 169 · see citing works
Survey on Classifying Spaces for Families of Subgroups
Lück, W. (2006) · Birkhäuser-Verlag eBooks · doi:10.1007/3-7643-7447-0_7 · Cited by 169 · see citing works
Hyperlinear and Sofic Groups: A Brief Guide
Pestov, V. (2008) · Bulletin of Symbolic Logic · doi:10.2178/bsl/1231081461 · Cited by 168 · see citing works
Graph Curvature for Differentiating Cancer Networks
Sandhu, R., Georgiou, T. T., Reznik, E., Zhu, L., Kolesov, I., Şenbabaoğlu, Y., & Tannenbaum, A. (2015) · Scientific Reports · doi:10.1038/srep12323 · Cited by 168 · see citing works
Low Distortion Delaunay Embedding of Trees in Hyperbolic Plane
Sarkar, R. (2012) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-25878-7_34 · Cited by 168 · see citing works
From Fractal Groups to Fractal Sets
Bartholdi, L., Grigorchuk, R. I., & Nekrashevych, V. (2003) · Birkhäuser Basel eBooks · doi:10.1007/978-3-0348-8014-5_2 · Cited by 162 · see citing works
Positive Curvature, Macroscopic Dimension, Spectral Gaps and Higher Signatures
Gromov, M. L. (1996) · Birkhäuser Boston eBooks · doi:10.1007/978-1-4612-4098-3_1 · Cited by 161 · see citing works
Self-citationEmergent Hyperbolic Network Geometry
Ginestra Bianconi, A., & Rahmede, C. (2017) · Scientific Reports · doi:10.1038/srep41974 · Cited by 158 · see citing works
Small cancellation theory and automatic groups
Gersten, S. M., & Short, H. (1990) · Inventiones mathematicae · doi:10.1007/bf01233430 · Cited by 157 · see citing works
Network geometry with flavor: From complexity to quantum geometry
Bianconi, G., & Rahmede, C. (2016) · Physical Review E · doi:10.1103/physreve.93.032315 · Cited by 150 · see citing works
Kahle, M. (2011) · Discrete & Computational Geometry · doi:10.1007/s00454-010-9319-3 · Cited by 150 · see citing works
Intrinsic Geometry of Surfaces
Aleksandrov, A. A., & Zalgaller, V. A. (2002) · Translations of mathematical monographs · doi:10.1090/mmono/015 · Cited by 148 · see citing works
The geometry of cube complexes and the complexity of their fundamental groups
Niblo, G. A., & Reeves, L. D. (1998) · Topology · doi:10.1016/s0040-9383(97)00018-9 · Cited by 148 · see citing works
Ricci curvature: An economic indicator for market fragility and systemic risk
Sandhu, R., Georgiou, T. T., & Tannenbaum, A. (2016) · Science Advances · doi:10.1126/sciadv.1501495 · Cited by 146 · see citing works
Davis, M. W., & Januszkiewicz, T. (1991) · Journal of Differential Geometry · doi:10.4310/jdg/1214447212 · Cited by 143 · see citing works
Tree-Like Structure in Large Social and Information Networks
Adcock, A. B., Sullivan, B. D., & Mahoney, M. W. (2013) · 2013 IEEE 13th International Conference on Data Mining · doi:10.1109/icdm.2013.77 · Cited by 141 · see citing works
Property (T) and rigidity for actions on Banach spaces
Bader, U., Furman, A., Gelander, T., & Monod, N. (2007) · Acta Mathematica · doi:10.1007/s11511-007-0013-0 · Cited by 140 · see citing works
Topologie de Gromov �quivariante, structures hyperboliques et arbres r�els
Paulin, F. (1988) · Inventiones mathematicae · doi:10.1007/bf01394344 · Cited by 140 · see citing works
A characterization of compact convex polyhedra in hyperbolic 3-space
Hodgson, C. D., & Rivin, I. (1993) · Inventiones mathematicae · doi:10.1007/bf01231281 · Cited by 140 · see citing works
Small cancellations over relatively hyperbolic groups and embedding theorems
Osin, D. (2010) · Annals of Mathematics · doi:10.4007/annals.2010.172.1 · Cited by 138 · see citing works
Automorphisms of Free Groups and Outer Space
Vogtmann, K. (2002) · Geometriae Dedicata · doi:10.1023/a:1020973910646 · Cited by 136 · see citing works
A barcode shape descriptor for curve point cloud data
Collins, A., Zomorodian, A., Carlsson, G., & Guibas, L. J. (2004) · Computers & Graphics · doi:10.1016/j.cag.2004.08.015 · Cited by 132 · see citing works
Finite index subgroups of graph products
Haglund, F. (2008) · Geometriae Dedicata · doi:10.1007/s10711-008-9270-0 · Cited by 131 · see citing works
The K-theoretic Farrell–Jones conjecture for hyperbolic groups
Bartels, A., Lück, W., & Reich, H. (2007) · Inventiones mathematicae · doi:10.1007/s00222-007-0093-7 · Cited by 130 · see citing works
Contracting elements and random walks
Sisto, A. (2016) · Journal für die reine und angewandte Mathematik (Crelles Journal) · doi:10.1515/crelle-2015-0093 · Cited by 128 · see citing works
Anosov representations and proper actions
Guéritaud, F., Guichard, O., Kassel, F., & Wienhard, A. (2017) · Geometry & Topology · doi:10.2140/gt.2017.21.485 · Cited by 128 · see citing works
Ozawa, N. (2004) · International Journal of Mathematics · doi:10.1142/s0129167x04002417 · Cited by 127 · see citing works
Interdisciplinary and physics challenges of network theory
Bianconi, G. (2015) · EPL (Europhysics Letters) · doi:10.1209/0295-5075/111/56001 · Cited by 126 · see citing works
A Survey on Centrality Metrics and Their Network Resilience Analysis
Wan, Z., Mahajan, Y., Kang, B. W., Moore, T. J., & Cho, J.-H. (2021) · IEEE Access · doi:10.1109/access.2021.3094196 · Cited by 126 · see citing works
On problems related to growth, entropy, and spectrum in group theory
Grigorchuk, R. I., & de la Harpe, P. (1997) · Journal of Dynamical and Control Systems · doi:10.1007/bf02471762 · Cited by 126 · see citing works
Hyperbolic Graph Attention Network
Zhang, Y., Wang, X., Shi, C., Jiang, X., & Ye, Y. F. (2021) · IEEE Transactions on Big Data · doi:10.1109/tbdata.2021.3081431 · Cited by 125 · see citing works
A topological characterisation of relatively hyperbolic groups
Yaman, A. (2004) · Journal für die reine und angewandte Mathematik (Crelles Journal) · doi:10.1515/crll.2004.007 · Cited by 125 · see citing works
Theorie du Potentiel sur les Graphes et les Varietes
Ancona, A. (1990) · Lecture notes in mathematics · doi:10.1007/bfb0103041 · Cited by 121 · see citing works
Combination of convergence groups
Dahmani, F. (2003) · Geometry & Topology · doi:10.2140/gt.2003.7.933 · Cited by 121 · see citing works
On Rigidity, Limit Sets, and End Invariants of Hyperbolic 3-Manifolds
Minsky, Y. N. (1994) · Journal of the American Mathematical Society · doi:10.1090/s0894-0347-1994-1257060-3 · Cited by 121 · see citing works
The geometry of the disk complex
Masur, H., & Schleimer, S. (2012) · Journal of the American Mathematical Society · doi:10.1090/s0894-0347-2012-00742-5 · Cited by 120 · see citing works
The pressure metric for Anosov representations
Bridgeman, M., Canary, R. D., Labourie, F., & Sambarino, A. (2015) · Geometric and Functional Analysis · doi:10.1007/s00039-015-0333-8 · Cited by 118 · see citing works
Solved and Unsolved Problems Around One Group
Grigorchuk, R. I. (2006) · Birkhäuser-Verlag eBooks · doi:10.1007/3-7643-7447-0_5 · Cited by 118 · see citing works
Bell, G., & Dranishnikov, A. N. (2008) · Topology and its Applications · doi:10.1016/j.topol.2008.02.011 · Cited by 118 · see citing works
CAT(-1)-spaces, divergence groups and their commensurators
Burger, M., & Mozes, S. (1996) · Journal of the American Mathematical Society · doi:10.1090/s0894-0347-96-00196-8 · Cited by 117 · see citing works
Baumslag, G., Gersten, S. M., Shapiro, M., & Short, H. (1991) · Journal of Pure and Applied Algebra · doi:10.1016/0022-4049(91)90139-s · Cited by 117 · see citing works
The K(π, 1)-Problem for Hyperplane Complements Associated to Infinite Reflection Groups
Charney, R. M., & Davis, M. W. (1995) · Journal of the American Mathematical Society · doi:10.1090/s0894-0347-1995-1303028-9 · Cited by 116 · see citing works
Hyperbolic Entailment Cones for Learning Hierarchical Embeddings
Ganea, O.-E., Bécigneul, G., & Hofmann, T. (2018) · arXiv · doi:10.48550/arxiv.1804.01882 · Cited by 115 · see citing works
Right-angled Artin groups are commensurable with right-angled Coxeter groups
Davis, M. W., & Januszkiewicz, T. (2000) · Journal of Pure and Applied Algebra · doi:10.1016/s0022-4049(99)00175-9 · Cited by 115 · see citing works
Orbihedra of nonpositive curvature
Ballmann, W., & Brin, M. (1995) · Publications mathématiques de l IHÉS · doi:10.1007/bf02698640 · Cited by 114 · see citing works
Acylindrical hyperbolicity of groups acting on trees
Minasyan, A., & Osin, D. (2014) · Mathematische Annalen · doi:10.1007/s00208-014-1138-z · Cited by 113 · see citing works
Extremal length estimates and product regions in Teichmüller space
Minsky, Y. N. (1996) · Duke Mathematical Journal · doi:10.1215/s0012-7094-96-08310-6 · Cited by 113 · see citing works
Gitik, R., Mitra, M., Rips, E., & Sageev, M. (1998) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-98-01792-9 · Cited by 109 · see citing works
The second bounded cohomology of word-hyperbolic groups
Epstein, D. B. A., & Fujiwara, K. (1997) · Topology · doi:10.1016/s0040-9383(96)00046-8 · Cited by 109 · see citing works
Trees and ultrametric spaces: a categorical equivalence
Hughes, B. (2004) · Advances in Mathematics · doi:10.1016/j.aim.2003.11.008 · Cited by 107 · see citing works
A topological characterisation of hyperbolic groups
Bowditch, B. H. (1998) · Journal of the American Mathematical Society · doi:10.1090/s0894-0347-98-00264-1 · Cited by 106 · see citing works
Yu, G. (1995) · K-Theory · doi:10.1007/bf00961664 · Cited by 105 · see citing works
Peripheral fillings of relatively hyperbolic groups
Osin, D. V. (2006) · Inventiones mathematicae · doi:10.1007/s00222-006-0012-3 · Cited by 103 · see citing works
Embeddings of graph braid and surface groups in right-angled Artin groups and braid groupsPreprint
Crisp, J., & Wiest, B. (2008) · Cited by 102 · see citing works
Olshanskii, A. Y., Osin, D., & Sapir, M. (2009) · Geometry & Topology · doi:10.2140/gt.2009.13.2051 · Cited by 101 · see citing works
Ricci curvature of the Internet topology
Ni, C.-C., Lin, Y.-Y., Gao, J., Gu, X. D., & Saucan, E. (2015) · IEEE Conference on Computer Communications (INFOCOM) · doi:10.1109/infocom.2015.7218668 · Cited by 101 · see citing works
INJECTIVE HULLS OF CERTAIN DISCRETE METRIC SPACES AND GROUPS
Lang, U. (2013) · Journal of Topology and Analysis · doi:10.1142/s1793525313500118 · Cited by 101 · see citing works
Groups acting on CAT(0) cube complexes
Niblo, G. A., & Reeves, L. (1997) · Geometry & Topology · doi:10.2140/gt.1997.1.1 · Cited by 100 · see citing works
Sous-groupes distingués et quotients des groupes hyperboliques
Delzant, T. (1996) · Duke Mathematical Journal · doi:10.1215/s0012-7094-96-08321-0 · Cited by 99 · see citing works
Emergent Complex Network Geometry
Wu, Z., Menichetti, G., Rahmede, C., & Bianconi, G. (2015) · Scientific Reports · doi:10.1038/srep10073 · Cited by 98 · see citing works
Combinatorial curvature for planar graphs
Higuchi, Y. (2001) · Journal of Graph Theory · doi:10.1002/jgt.10004 · Cited by 97 · see citing works
Group cohomology with lipschitz control and higher signatures
Alain Connes, A., Gromov, M. L., & Moscovici, H. (1993) · Geometric and Functional Analysis · doi:10.1007/bf01895513 · Cited by 97 · see citing works
Self-citationRandom walks on the mapping class group
Maher, J. (2011) · Duke Mathematical Journal · doi:10.1215/00127094-2010-216 · Cited by 97 · see citing works
Geodesic automation and growth functions for Artin groups of finite type
Charney, R. M. (1995) · Mathematische Annalen · doi:10.1007/bf01446631 · Cited by 97 · see citing works
ELEMENTARY SUBGROUPS OF RELATIVELY HYPERBOLIC GROUPS AND BOUNDED GENERATION
Osin, D. (2006) · International Journal of Algebra and Computation · doi:10.1142/s0218196706002901 · Cited by 94 · see citing works
Bounds on exceptional Dehn filling
Agol, I. (2000) · Geometry & Topology · doi:10.2140/gt.2000.4.431 · Cited by 94 · see citing works
- Authors
- Gromov, M.
- Corresponding author
- Gromov, M.
- Venue
- Mathematical Sciences Research Institute Publications
- Publisher
- Springer New York
- Published
- 1987
- Pages
- 75-263
- ISSN
- 0940-4740 (ISSN-L)
- OpenAlex
- W4235484205
- Cited by
- 1,817
- References
- 19
- Citations by year
- 2026: 41 · 2025: 106 · 2024: 94 · 2023: 92 · 2022: 87 · 2021: 90 · 2020: 72 · 2019: 69 · 2018: 72 · 2017: 82 · 2016: 79 · 2015: 75 · 2014: 68 · 2013: 66 · 2012: 54
- FWCI
- 19.75
- Type
- book chapter
- Language
- en
- Open access
- closed
- Locations
- Mathematical Sciences Research Institute publications (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Physical Sciences › Mathematics › Applied Mathematics › Geometric Analysis and Curvature Flows
- Physical Sciences › Mathematics › Geometry and Topology › Mathematics and Applications
- Keywords
- hyperbolic groups, Gromov hyperbolicity, geometric group theory, Cayley graphs, word metric, hyperbolic geometry
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
