Mapping class group representations from Drinfeld doubles of finite groups

2015/06/10 by Jens Fjelstad, Fjelstad, Jens, Jürgen Fuchs +1 · 1 citation
Mathematics · Physics and Astronomy · #57M99 #57R56 #81R50 #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #hep-th #math-ph #math.GT #math.MP #math.QA #msc:57M99 #msc:57R56 #msc:81R50

paper · pdf · doi:10.48550/arxiv.1506.03263

68 pages, several figures. v2: 60 pages; removed a few examples and rearranged the presentation of the remaining examples

openalex publication_date 2015/06/10 · arxiv created 2020/05/11 · arxiv updated 2020/05/12 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

We investigate representations of mapping class groups of surfaces that arise from the untwisted Drinfeld double of a finite group G, focusing on surfaces without marked points or with one marked point. We obtain concrete descriptions of such representations in terms of finite group data. This allows us to establish various properties of these representations. In particular we show that they have finite images, and that for surfaces of genus at least 3 their restriction to the Torelli group is non-trivial iff G is non-abelian.

Cited by

• Modular fusion categories with trivial Torelli group actions

Related

• Representations of the mapping class group of a non-orientable surface
• Finiteness of Mapping Class Group Representations from Twisted Dijkgraaf-Witten Theory
• Representations of surface groups with finite mapping class group orbits
• A finite presentation of the mapping class group of an oriented surface
• The versatility of the Drinfeld double of a finite group