Rigidity and Flexibility for Handlebody Groups

Sebastian Hensel

Rigidity and Flexibility for Handlebody Groups

Geometric Topology 2016-08-11 v1 Group Theory

Authors: Sebastian Hensel

Abstract

We show that finite index subgroups of the handlebody group are rigid in their ambient mapping class group: any injective map of a finite index subgroup of the genus $g$ handlebody group into the genus $g$ mapping class group is conjugation by a mapping class group element. On the other hand, we construct an injection of the genus $g$ handlebody group into a genus $h>g$ mapping class group which is not conjugate into a handlebody group.

Keywords

mapping class groups of surfaces finite group theory conjugacy classes in groups

Cite

@article{arxiv.1608.03094,
  title  = {Rigidity and Flexibility for Handlebody Groups},
  author = {Sebastian Hensel},
  journal= {arXiv preprint arXiv:1608.03094},
  year   = {2016}
}

Comments

21 pages, 4 figures

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