Cosets of monodromies and quantum representations

DOI10.1512/iumj.2022.71.8971zbMath1500.57014arXiv2001.04518OpenAlexW3000020740MaRDI QIDQ5093771

Efstratia Kalfagianni, Renaud Detcherry

Publication date: 1 August 2022

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.04518

zbMATH Keywords

mapping class groupsopen book decompositionquantum representation

Mathematics Subject Classification ID

2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) (57K20) Invariants of 3-manifolds (including skein modules, character varieties) (57K31)

Cites Work

• All finite groups are involved in the mapping class group
• Abelian and solvable subgroups of the mapping class group
• The Nielsen-Thurston classification of mapping classes is determined by TQFT
• Turaev-Viro invariants, colored Jones polynomials, and volume
• An application of TQFT to modular representation theory
• On the asymptotic expansion of the quantum SU(2) invariant at \(q =exp(4{\pi}\sqrt{-1}/N\)) for closed hyperbolic 3-manifolds obtained by integral surgery along the figure-eight knot
• Geometry of the complex of curves. I: Hyperbolicity
• How to construct all fibered knots and links
• Groups generated by positive multi-twists and the fake lantern problem
• Quantum representations and monodromies of fibered links
• Invariants of 3-manifolds via link polynomials and quantum groups
• Links with no exceptional surgeries
• Stabilizing the monodromy of an open book decomposition
• Dehn filling, volume, and the Jones polynomial
• Asymptotic faithfulness of the quantum \(\text{SU}(n)\) representations of the mapping class groups
• On the stable equivalence of open books in three-manifolds
• Quotients of surface groups and homology of finite covers via quantum representations
• The homological content of the Jones representations at q = −1
• Homology Cobordisms, Link Concordances, and Hyperbolic 3-Manifolds
• Topological Quantum Field Theory and the Nielsen–Thurston classification of $M(0,4)$
• 3-manifolds efficiently bound 4-manifolds
• A "Tits-Alternative" for Subgroups of Surface Mapping Class Groups
• LIMITS OF THE QUANTUM SO(3) REPRESENTATIONS FOR THE ONE-HOLED TORUS
• Growth of Turaev–Viro invariants and cabling
• Action of M(0,2n) on some kernel spaces coming from SU (2)-TQFT

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