From pure braid groups to hyperbolic groups
Lei Chen
University of Maryland, College Park, USA

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 (2019) 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 this article
Lei Chen, From pure braid groups to hyperbolic groups. Enseign. Math. 71 (2025), no. 1/2, pp. 71–85
DOI 10.4171/LEM/1068