GEOMETRIC CONSTRUCTION OF MODULAR FUNCTORS FROM CONFORMAL FIELD THEORY

DOI10.1142/S0218216507005233zbMath1123.81041arXivmath/0306235WikidataQ56814532 ScholiaQ56814532MaRDI QIDQ3435255

Kenji Ueno, Jørgen Ellegaard Andersen

Publication date: 25 April 2007

Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0306235

zbMATH Keywords

conformal field theoryTeichmüller spaceRiemann surfacemodular functoraffine Lie algebratopological quantum field theoryprojectively flat connetion

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Applications of Lie (super)algebras to physics, etc. (17B81) Topological field theories in quantum mechanics (81T45) Topological quantum field theories (aspects of differential topology) (57R56)

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Cites Work

• Unnamed Item
• On framings of 3-manifolds
• Geometric realization of conformal field theory on Riemann surfaces
• Three-manifold invariants derived from the Kauffman bracket
• Hecke algebras, modular categories and 3-manifolds quantum invariants
• Theta functions on Riemann surfaces
• Topological quantum field theories derived from the Kauffman bracket
• Non-additivity of the signature
• CONSTRUCTING TQFTS FROM MODULAR FUNCTORS
• Quantum invariants of knots and 3-manifolds