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  Cosets of monodromies and quantum representations

Detcherry, R., & Kalfagianni, E. (2022). Cosets of monodromies and quantum representations. Indiana University Mathematics Journal, 71(3), 1101-1129. doi:10.1512/iumj.2022.71.8971.

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 Creators:
Detcherry, Renaud1, Author           
Kalfagianni, Efstratia, Author
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Geometric Topology, Quantum Algebra
 Abstract: We use geometric methods to show that given any $3$-manifold $M$, and $g$ a
sufficiently large integer, the mapping class group
$\mathrm{Mod}(\Sigma_{g,1})$ contains a coset of an abelian subgroup of rank
$\lfloor \frac{g}{2}\rfloor,$ consisting of pseudo-Anosov monodromies of
open-book decompositions in $M.$ We prove a similar result for rank two free
cosets of $\mathrm{Mod}(\Sigma_{g,1}).$ These results have applications to a
conjecture of Andersen, Masbaum and Ueno about quantum representations of
surface mapping class groups. For surfaces with boundary, and large enough
genus, we construct cosets of abelian and free subgroups of their mapping class
groups consisting of elements that satisfy the conjecture. The mapping tori of
these elements are fibered 3-manifolds that satisfy a weak form of the
Turaev-Viro invariants volume conjecture.

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Language(s): eng - English
 Dates: 2022
 Publication Status: Issued
 Pages: 29
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 2001.04518
DOI: 10.1512/iumj.2022.71.8971
 Degree: -

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Title: Indiana University Mathematics Journal
Source Genre: Journal
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Publ. Info: Indiana University
Pages: - Volume / Issue: 71 (3) Sequence Number: - Start / End Page: 1101 - 1129 Identifier: -