The DOI matches its Crossref record; 19 of the 19 references it cites were found in a registry or an index.
Invariants of piecewise-linear 3-manifolds
Open accessAbstract
This paper presents an algebraic framework for constructing invariants of closed oriented 3-manifolds by taking a state sum model on a triangulation. This algebraic framework consists of a tensor category with a condition on the duals which we have called a spherical category. A significant feature is that the tensor category is not required to be braided. The main examples are constructed from the categories of representations of involutive Hopf algebras and of quantised enveloping algebras at a root of unity.
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Cites
Invariants of 3-manifolds via link polynomials and quantum groups
Reshetikhin, N., & Turaev, V. G. (1991) · Inventiones Mathematicae · doi:10.1007/bf01239527 · Cited by 1,492
State sum invariants of 3-manifolds and quantum 6j-symbols
Turaev, V. G., & Viro, O. Y. (1992) · Topology · doi:10.1016/0040-9383(92)90015-a · Cited by 1,145
Introduction to Piecewise-Linear Topology
Rourke, C. P., & Sanderson, B. J. (1972) · Springer eBooks · doi:10.1007/978-3-642-81735-9 · Cited by 1,047
Ribbon graphs and their invaraints derived from quantum groups
Reshetikhin, N. Y., & Turaev, V. G. (1990) · Communications in Mathematical Physics · doi:10.1007/bf02096491 · Cited by 1,010
Quantum Invariants of Knots and 3-Manifolds
Turaev, V. G. (2010) · De Gruyter eBooks · doi:10.1515/9783110221848 · Cited by 841
Quantum Invariants of Knots and 3-Manifolds
Turaev, V. G. (1994) · doi:10.1515/9783110883275 · Cited by 832
The geometry of tensor calculus, I
Joyal, A., & Street, R. (1991) · Advances in Mathematics · doi:10.1016/0001-8708(91)90003-p · Cited by 660
Coherence for compact closed categories
Kelly, G. M., & Laplaza, M. L. (1980) · Journal of Pure and Applied Algebra · doi:10.1016/0022-4049(80)90101-2 · Cited by 437
P.L. Homeomorphic Manifolds are Equivalent by Elementary 5hellingst
Pachner, U. (1991) · European Journal of Combinatorics · doi:10.1016/s0195-6698(13)80080-7 · Cited by 344
REPRESENTATIONS Of THE ALGEBRA Uq(sl(2)), q-ORTHOGONAL POLYNOMIALS AND INVARIANTS OF LINKS
Kirillov, A. N., & Reshetikhin, N. Y. (1990) · Advanced Series in Mathematical Physics · doi:10.1142/9789812798329_0012 · Cited by 297
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Oriti, D. (2001) · Reports on Progress in Physics · doi:10.1088/0034-4885/64/12/203 · Cited by 201
Barrett, J. W., & Naish-Guzman, I. (2009) · Classical and Quantum Gravity · doi:10.1088/0264-9381/26/15/155014 · Cited by 131
Self-citationSpin foam diagrammatics and topological invariance
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Metadata
- Authors
- Barrett, J., & Westbury, B.
- Venue
- Transactions of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Published
- 1996
- Volume
- 348
- Issue
- 10
- Pages
- 3997-4022
- ISSN
- 0002-9947 (ISSN-L)
- 1088-6850
- OpenAlex
- W1491726941
- Cited by
- 318
- References
- 19
- FWCI
- 5.86
- Type
- journal article
- Language
- en
- Open access
- bronze
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
