On mapping class group quotients by powers of Dehn twists and their representations

DOI10.4171/IRMA/33-1/15zbMATH Open1478.57016arXiv2009.05961OpenAlexW3086940205MaRDI QIDQ2055085

Louis Funar

Publication date: 3 December 2021

Abstract: The aim of this paper is to survey some known results about mapping class group quotients by powers of Dehn twists, related to their finite dimensional representations and to state some open questions. One can construct finite quotients of them, out of representations with Zariski dense images into semisimple Lie groups. We show that, in genus 2, the Fibonacci TQFT representation is actually a specialization of the Jones representation. Eventually, we explain a method of Long and Moody which provides large families of mapping class group representations.

Full work available at URL: https://arxiv.org/abs/2009.05961

zbMATH Keywords

surveyfinite dimensional representationsDehn twistsJones representationFibonacci TQFT representationmapping class group quotients

Mathematics Subject Classification ID

Braid groups; Artin groups (20F36) Topological methods in group theory (57M07) Other groups related to topology or analysis (20F38) Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes (57-02) Research exposition (monographs, survey articles) pertaining to group theory (20-02) 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) (57K20)

Related Items (2)

Dehn twists and free subgroups of symplectic mapping class groups ⋮ Presentations of cluster modular groups and generation by cluster Dehn twists

This page was built for publication: On mapping class group quotients by powers of Dehn twists and their representations

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q2055085)