A combinatorial take on hierarchical hyperbolicity and applications to quotients of mapping class groups

Autor:	Behrstock, Jason, Hagen, Mark, Martin, Alexandre, Sisto, Alessandro
Rok vydání:	2020
Předmět:	Mathematics - Group Theory Mathematics - Geometric Topology
Druh dokumentu:	Working Paper
Popis:	We give a simple combinatorial criterion, in terms of an action on a hyperbolic simplicial complex, for a group to be hierarchically hyperbolic. We apply this to show that quotients of mapping class groups by large powers of Dehn twists are hierarchically hyperbolic (and even relatively hyperbolic in the genus 2 case). Under residual finiteness assumptions, we construct many non-elementary hyperbolic quotients of mapping class groups. Using these quotients, we reduce questions of Reid and Bridson-Reid-Wilton about finite quotients of mapping class groups to residual finiteness of specific hyperbolic groups. Comment: Revised according to referee comments. This version accepted in Journal of Topology
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2005.00567 Zobrazit plný text záznamu View this record from Arxiv