Largest hyperbolic actions of 3--manifold groups
Geometric Topology
2023-05-15 v1
Abstract
The set of equivalence classes of cobounded actions of a group G on different hyperbolic metric spaces carries a natural partial order. Following Abbott--Balasubramanya--Osin, the group G is H--accessible if the resulting poset has a largest element. In this paper, we prove that every non-geometric 3--manifold has a finite cover with H--inaccessible fundamental group and give conditions under which the fundamental group of the original manifold is H--inaccessible. We also prove that every Croke--Kleiner admissible group (a class of graphs of groups that generalizes fundamental groups of 3--dimensional graph manifolds) has a finite index subgroup that is H--inaccessible.
Cite
@article{arxiv.2305.07425,
title = {Largest hyperbolic actions of 3--manifold groups},
author = {Carolyn Abbott and Hoang Thanh Nguyen and Alexander J. Rasmussen},
journal= {arXiv preprint arXiv:2305.07425},
year = {2023}
}