From pure braid groups to hyperbolic groups

  • Lei Chen

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

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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. (2024), published online first

DOI 10.4171/LEM/1068