The DOI matches its Crossref record; 28 of the 29 references it cites were found in a registry or an index.
Simplicial homotopy theory
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“sense that a continuous map f : X → Y induces a map of sets π 0 (f ) : π 0 (X) → π 0 (Y ), satisfying certain obvious conditions on composite maps and identity maps.”
From Topology and data (2009) · cites this paper as [19]
Citations
Cites
Foundations of Algebraic Topology
Eilenberg, S., & Steenrod, N. E. (1952) · Princeton University Press eBooks · doi:10.1515/9781400877492 · Cited by 1,660
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Quillen, D. G. (1967) · Lecture notes in mathematics · doi:10.1007/bfb0097438 · Cited by 920
Adams, J. F. (1966) · Topology · doi:10.1016/0040-9383(66)90004-8 · Cited by 589
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The Geometric Realization of a Semi-Simplicial Complex
Milnor, J. (1957) · Annals of Mathematics · doi:10.2307/1969967 · Cited by 284
Homologie nicht-additiver Funktoren. Anwendungen
Dold, A., & Puppe, D. (1961) · Annales de l’institut Fourier · doi:10.5802/aif.114 · Cited by 279
Homology of Symmetric Products and Other Functors of Complexes
Dold, A. (1958) · Annals of Mathematics · doi:10.2307/1970043 · Cited by 274
On the structure and applications of the steenrod algebra
Adams, J. F. (1958) · Commentarii Mathematici Helvetici · doi:10.1007/bf02564578 · Cited by 233
Adams, J. F. (1956) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.42.7.409 · Cited by 231
A Combinatorial Definition of Homotopy Groups
Kan, D. M. (1958) · Annals of Mathematics · doi:10.2307/1970006 · Cited by 206
The mod-p lower central series and the Adams spectral sequence
Bousfield, A. K., Curtis, E. B., Kan, D. M., Quillen, D. G., Rector, D. L., & Schlesinger, J. W. (1966) · Topology · doi:10.1016/0040-9383(66)90024-3 · Cited by 199
Self-citationSemi-Simplicial Complexes and Singular Homology
Eilenberg, S., & Zilber, J. A. (1950) · Annals of Mathematics · doi:10.2307/1969364 · Cited by 186
Relations Between Homology and Homotopy Groups of Spaces
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Kan, D. M. (1957) · American Journal of Mathematics · doi:10.2307/2372558 · Cited by 118
Eilenberg, S. (1944) · The Annals of Mathematics · doi:10.2307/1969185 · Cited by 113
Méthode Simpliciale en Algèbre Homologique et Algèbre Commutative
André, M. (1967) · Lecture notes in mathematics · doi:10.1007/bfb0077199 · Cited by 106
On Homotopy Theory and C.S.S. Groups
Kan, D. M. (1958) · Annals of Mathematics · doi:10.2307/1970042 · Cited by 92
Some Relations Between Homotopy and Homology
Curtis, E. B. (1965) · Annals of Mathematics · doi:10.2307/1970703 · Cited by 72
Self-citationOn Semisimplicial Fibre-Bundles
Barratt, M. G., Gugenheim, V. K. A. M., & Moore, J. C. (1959) · American Journal of Mathematics · doi:10.2307/2372920 · Cited by 57
Semisimpliziale algebraische Topologie
Lamotke, K. (1968) · Springer eBooks · doi:10.1007/978-3-662-12988-3 · Cited by 51
The geometric realization of a Kan fibration is a Serre fibration
Quillen, D. G. (1968) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-1968-0238322-1 · Cited by 31
An unstable Adams spectral sequence
Rector, D. L. (1966) · Topology · doi:10.1016/0040-9383(66)90025-5 · Cited by 30
Lower central series of semi-simplicial complexes
Curtis, E. B. (1963) · Topology · doi:10.1016/0040-9383(63)90030-2 · Cited by 25
Self-citationSome nonzero homotopy groups of spheres
Curtis, E. B. (1969) · Bulletin of the American Mathematical Society · doi:10.1090/s0002-9904-1969-12236-6 · Cited by 25
Self-citationThe semi-simplicial free Lie ring
Schlesinger, J. W. (1966) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-1966-0199861-8 · Cited by 16
On the order of the image of J
Mahowald, M. E. (1967) · Topology · doi:10.1016/0040-9383(67)90024-9 · Cited by 15
Fritsch, R., & Puppe, D. (1967) · Archiv der Mathematik · doi:10.1007/bf01899490 · Cited by 9
Cited by
Sorted by citations
Carlsson, G. (2009) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-09-01249-x · Cited by 2,302
“It is the basis for many comparison theorems in topology, and in fact underlies the combinatorization of topology obtained via simplicial sets [45], [19].”
BackgroundHovey, M. A., Shipley, B. E., & Smith, J. (1999) · Journal of the American Mathematical Society · doi:10.1090/s0894-0347-99-00320-3 · Cited by 588
Van Kampen theorems for diagrams of spaces
Ronald Brown, A., & Loday, J.-L. (1987) · Topology · doi:10.1016/0040-9383(87)90004-8 · Cited by 400
Quadratic functions in geometry, topology, and M-theory
Hopkins, M. J., & Singer, I. M. (2005) · Journal of Differential Geometry · doi:10.4310/jdg/1143642908 · Cited by 328
Algebraic $K$-theory and etale cohomology
Thomason, R. W. (1985) · Annales Scientifiques de l École Normale Supérieure · doi:10.24033/asens.1495 · Cited by 302
Metadata
- Authors
- Curtis, E. B.
- Affiliations
- Aarhus University (DK)
- Corresponding author
- Curtis, Edward B
- ORCID
- Curtis, Edward B
- Venue
- Advances in Mathematics
- Publisher
- Elsevier BV
- Published
- 1971-04
- Volume
- 6
- Issue
- 2
- Pages
- 107-209
- ISSN
- 0001-8708 (ISSN-L)
- OpenAlex
- W1971238472
- Cited by
- 304
- References
- 29
- Citations by year
- 2026: 6 · 2025: 3 · 2024: 7 · 2023: 8 · 2022: 7 · 2021: 9 · 2020: 3 · 2019: 6 · 2018: 15 · 2017: 4 · 2016: 7 · 2015: 5 · 2014: 9 · 2013: 10 · 2012: 19
- FWCI
- 2.34
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Advances in Mathematics (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Homotopy and Cohomology in Algebraic Topology
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Advanced Combinatorial Mathematics
- Keywords
- simplicial sets, simplicial homotopy theory, homotopy theory
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