Commentarii Mathematici Helvetici


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Volume 93, Issue 2, 2018, pp. 335–358
DOI: 10.4171/CMH/436

Published online: 2018-05-31

Rigidity and flexibility for handlebody groups

Sebastian Hensel[1]

(1) Universit├Ąt Bonn, Germany

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, handlebody groups, commensurator, rigidity

Hensel Sebastian: Rigidity and flexibility for handlebody groups. Comment. Math. Helv. 93 (2018), 335-358. doi: 10.4171/CMH/436