The Nielsen-Thurston classification of mapping classes is determined by TQFT

DOI10.1215/KJM/1250271414zbMath1195.57065arXivmath/0605036OpenAlexW1644486896MaRDI QIDQ1012026

Jørgen Ellegaard Andersen

Publication date: 14 April 2009

Published in: Journal of Mathematics of Kyoto University (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0605036

zbMATH Keywords

Teichmüller spacemoduli spacemapping classesoriented surfaceNielsen-Thurston classificationBHMV skein modelPseudo-Anosov

Mathematics Subject Classification ID

General low-dimensional topology (57M99) Topological field theories in quantum mechanics (81T45) Topological quantum field theories (aspects of differential topology) (57R56) Group actions on manifolds and cell complexes in low dimensions (57M60) Teichmüller theory for Riemann surfaces (30F60) Geometric quantization (53D50) Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) (14D21)

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Asymptotics of the Hilbert-Schmidt norm of curve operators in TQFT ⋮ Cosets of monodromies and quantum representations ⋮ Modular functors are determined by their genus zero data ⋮ Hitchin's connection, Toeplitz operators, and symmetry invariant deformation quantization ⋮ Hitchin's connection in metaplectic quantization ⋮ The Witten-Reshetikhin-Turaev invariants of finite order mapping tori. II. ⋮ Construction of the Witten-Reshetikhin-Turaev TQFT from conformal field theory ⋮ Quantum representations and monodromies of fibered links ⋮ A TQFT from quantum Teichmüller theory ⋮ Formal connections for families of star products

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