JournalscmhVol. 93, No. 2pp. 335–358

Rigidity and flexibility for handlebody groups

  • Sebastian Hensel

    Universität Bonn, Germany
Rigidity and flexibility for handlebody groups cover

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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 gg handlebody group into the genus gg mapping class group is conjugation by a mapping class group element.

On the other hand, we construct an injection of the genus gg handlebody group into a genus h>gh > g mapping class group which is not conjugate into a handlebody group.

Cite this article

Sebastian Hensel, Rigidity and flexibility for handlebody groups. Comment. Math. Helv. 93 (2018), no. 2, pp. 335–358

DOI 10.4171/CMH/436