The DOI matches its Crossref record; 18 of the 18 references it cites were found in a registry or an index.
Higher-dimensional algebra and topological quantum field theory
Open accessAbstract
The study of topological quantum field theories increasingly relies upon concepts from higher-dimensional algebra such as n-categories and n-vector spaces. We review progress towards a definition of n-category suited for this purpose, and outline a program in which n-dimensional topological quantum field theories (TQFTs) are to be described as n-category representations. First we describe a ‘‘suspension’’ operation on n-categories, and hypothesize that the k-fold suspension of a weak n-category stabilizes for k≥n+2. We give evidence for this hypothesis and describe its relation to stable homotopy theory. We then propose a description of n-dimensional unitary extended TQFTs as weak n-functors from the ‘‘free stable weak n-category with duals on one object’’ to the n-category of ‘‘n-Hilbert spaces.’’ We conclude by describing n-categorical generalizations of deformation quantization and the quantum double construction.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
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
Topological gauge theories and group cohomology
Dijkgraaf, R., & Witten, E. (1990) · Communications in Mathematical Physics · doi:10.1007/bf02096988 · Cited by 1,106
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
Topological quantum field theory
Atiyah, M. F. (1988) · Publications Mathématiques de l'IHÉS · doi:10.1007/bf02698547 · Cited by 976
Natural Associativity and Commutativity
Lane, S. M. (1979) · Springer eBooks · doi:10.1007/978-1-4615-7831-4_19 · Cited by 561
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
From Groups to Groupoids: a Brief Survey
Brown, R. (1987) · Bulletin of the London Mathematical Society · doi:10.1112/blms/19.2.113 · Cited by 324
New points of view in knot theory
Birman, J. S. (1993) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-1993-00389-6 · Cited by 298
Braided compact closed categories with applications to low dimensional topology
Freyd, P. J., & Yetter, D. N. (1989) · Advances in Mathematics · doi:10.1016/0001-8708(89)90018-2 · Cited by 281
Four-dimensional topological quantum field theory, Hopf categories, and the canonical bases
Crane, L., & Frenkel, I. B. (1994) · Journal of Mathematical Physics · doi:10.1063/1.530746 · Cited by 268
Cited by
Baez, J. C. (1998) · Classical and Quantum Gravity · doi:10.1088/0264-9381/15/7/004 · Cited by 381
Self-citationLinking topological quantum field theory and nonperturbative quantum gravity
Smolin, L. (1995) · Journal of Mathematical Physics · doi:10.1063/1.531251 · Cited by 234
The geometry of quantum spin networks
Borissov, R., Major, S., & Smolin, L. (1996) · Classical and Quantum Gravity · doi:10.1088/0264-9381/13/12/009 · Cited by 68
Quantum gravity as a “sum over surfaces”
Rovelli, C. (1997) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/s0920-5632(97)00351-4 · Cited by 18
Metadata
- Authors
- Baez, J. C., & Dolan, J.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1995-11-01
- Volume
- 36
- Issue
- 11
- Pages
- 6073-6105
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W2070886143
- Cited by
- 317
- References
- 18
- FWCI
- 8.19
- Type
- journal article
- Language
- en
- Open access
- green
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
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Higher-dimensional algebra and topological quantum field theory. https://app.cochat.ai/papers/10.1063/1.531236
- The paper
- Baez, J. C., & Dolan, J. (1995). Higher-dimensional algebra and topological quantum field theory. Journal of Mathematical Physics. https://doi.org/10.1063/1.531236
Data sources
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.
