A combinatorial take on hierarchical hyperbolicity and applications to quotients of mapping class groups
2020
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. 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.
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
66
References
11
Citations
NaN
KQI