Quasi-morphisms on surface diffeomorphism groups
Geometric Topology
2020-03-31 v2 Differential Geometry
Group Theory
Metric Geometry
Abstract
We show that the identity component of the group of diffeomorphisms of a closed oriented surface of positive genus admits many unbounded quasi-morphisms. As a corollary, we also deduce that this group is not uniformly perfect and its fragmentation norm is unbounded, answering a question of Burago--Ivanov--Polterovich. As a key tool we construct a hyperbolic graph on which these groups act, which is the analog of the curve graph for the mapping class group.
Cite
@article{arxiv.1909.07164,
title = {Quasi-morphisms on surface diffeomorphism groups},
author = {Jonathan Bowden and Sebastian Hensel and Richard Webb},
journal= {arXiv preprint arXiv:1909.07164},
year = {2020}
}
Comments
19 pages, no figures