State sum invariants of 4-manifolds
Abstract
We provide, with proofs, a complete description of the authors' construction of state-sum invariants announced in [CY], and its generalization to an arbitrary (artinian) semisimple tortile category. We also discuss the relationship of these invariants to generalizations of Broda's surgery invariants [Br1,Br2] using techniques developed in the case of the semi-simple sub-quotient of Rep(U q(sl 2)) (q a principal 4r th root of unity) by Roberts [Ro1]. We briefly discuss the generalizations to invariants of 4-manifolds equipped with 2-dimensional (co)homology classes introduced by Yetter [Y6] and Roberts [Ro2].
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The new state sum is already very close to a topological theory, in that the deviation from the topological theory [4] is only in the imposed constraints.
“However, it is already very close to a topological theory, in that the deviation from the topological theory [4] is only in the imposed constraints.”
From Relativistic spin networks and quantum gravity (1998) · cites this paper as [4]
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References 32 · Cited by 139
- Authors
- Crane, L., Kauffman, L. H., & Yetter, D. N.
- Affiliations
- Kansas State University (US)
- University of Illinois Chicago (US)
- Venue
- Journal of Knot Theory and Its Ramifications
- Publisher
- World Scientific Pub Co Pte Lt
- Published
- 1997-04
- Volume
- 06
- Issue
- 02
- Pages
- 177-234
- ISSN
- 0218-2165 (ISSN-L)
- 1793-6527
- OpenAlex
- W2153761775
- Cited by
- 139
- References
- 32
- Citations by year
- 2026: 4 · 2025: 4 · 2024: 4 · 2023: 3 · 2022: 6 · 2021: 7 · 2020: 3 · 2019: 5 · 2018: 6 · 2017: 4 · 2016: 2 · 2015: 2 · 2014: 1 · 2013: 2 · 2012: 5
- FWCI
- 16.72
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Knot Theory and Its Ramifications (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Physical Sciences › Mathematics › Mathematical Physics › Homotopy and Cohomology in Algebraic Topology
- Physical Sciences › Mathematics › Geometry and Topology › Algebraic structures and combinatorial models
- Keywords
- state-sum invariants, 4-manifolds, quantum invariants, roots of unity, 4-manifold topology
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