The Dehn Twist Action for Quantum Representations of Mapping Class Groups

Autor:	Müller, Lukas, Woike, Lukas
Rok vydání:	2023
Předmět:	Mathematics - Quantum Algebra Mathematics - Geometric Topology Mathematics - Representation Theory
Druh dokumentu:	Working Paper
Popis:	We calculate the Dehn twist action on the spaces of conformal blocks of a not necessarily semisimple modular category. In particular, we give the order of the Dehn twists under the mapping class group representations of closed surfaces. For Dehn twists about non-separating simple closed curves, we prove that this order is the order of the ribbon twist, thereby generalizing a result that De Renzi-Gainutdinov-Geer-Patureau-Mirand-Runkel obtained for the small quantum group. In the separating case, we express the order using the order of the ribbon twist on monoidal powers of the canonical end. As an application, we prove that the Johnson kernel of the mapping class group acts trivially if and only if for the canonical end the ribbon twist and double braiding with itself are trivial. We give a similar result for the visibility of the Torelli group. Comment: 20 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2311.16020 Zobrazit plný text záznamu View this record from Arxiv