From pure braid groups to hyperbolic groups

Lei Chen

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arXiv · 2007.15178

From pure braid groups to hyperbolic groups

Lei Chen

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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 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.

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Lei Chen. 2020-07-30. From pure braid groups to hyperbolic groups. https://arxiv.org/abs/2007.15178

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