Invariants of 3-manifolds via link polynomials and quantum groups
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Matrix models were first created to formulate two-dimensional quantum gravity, then Boulatov extended them to three dimensions where the model yields the Ponzano-Regge-Turaev-Viro spin foam formulation of 3D quantum gravity, and Ooguri extended them to four dimensions where the model yields the Crane-Yetter spin foam formulation of 4D BF theory.
“Matrix models were invented more than 15 years ago to give a precise formulation of 2D quantum gravity (or 'zero-dimensional string theory') [83][84][85][86][87], then generalized to three dimensions by Boulatov [88], whose model gives the Ponzano-Regge-Turaev-Viro (spin foam) formulation of 3D quantum gravity (still a topological theory)”
From Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity (2001) · cites this paper as [88]
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- Authors
- Reshetikhin, N., & Turaev, V. G.
- Affiliations
- Harvard University (US)
- Venue
- Inventiones Mathematicae
- Published
- 1991-12
- Volume
- 103
- Issue
- 1
- Pages
- 547-597
- ISSN
- 0020-9910 (ISSN-L)
- 1432-1297
- OpenAlex
- W2080743555
- Cited by
- 1,492
- References
- 22
- Citations by year
- 2026: 34 · 2025: 64 · 2024: 41 · 2023: 104 · 2022: 54 · 2021: 66 · 2020: 47 · 2019: 42 · 2018: 48 · 2017: 35 · 2016: 56 · 2015: 35 · 2014: 41 · 2013: 46 · 2012: 47
- FWCI
- 62.60
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Inventiones mathematicae (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Physical Sciences › Mathematics › Geometry and Topology › Algebraic structures and combinatorial models
- Physical Sciences › Mathematics › Mathematical Physics › Homotopy and Cohomology in Algebraic Topology
- Keywords
- 3-manifolds, link polynomials, quantum groups, knot theory, quantum invariants
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