From pure braid groups to hyperbolic groups
Geometric Topology
2020-07-31 v1
Abstract
In this note we show that any homomorphism from a pure surface braid group to a torsion-free hyperbolic group either has a cyclic image or factors through a forgetful map. This extends and gives a new proof of an earlier result of the author which works only when the target is a free group or a surface group. We also prove a similar rigidity result for the pure braid group of the disk.
Cite
@article{arxiv.2007.15178,
title = {From pure braid groups to hyperbolic groups},
author = {Lei Chen},
journal= {arXiv preprint arXiv:2007.15178},
year = {2020}
}
Comments
14 pages, 4 figures