## Advanced Studies in Pure Mathematics

- Adv. Stud. Pure Math.
- Hyperbolic Geometry and Geometric Group Theory, K. Fujiwara, S. Kojima and K. Ohshika, eds. (Tokyo: Mathematical Society of Japan, 2017), 13 - 36

### One-ended subgroups of mapping class groups

#### Abstract

Suppose we have a one-ended finitely presented group with a purely loxodromic action on a Gromov hyperbolic space satisfying an acylindricity condition. We show that, given a finite generating set, there is an automorphism of the group, and some point in the space which is moved a bounded distance by each of the images of the generators under the automorphism. Here the bound depends only on the group, generating set, and constants of hyperbolicity and acylindricity. With results from elsewhere, this implies that, up to conjugacy, there can only be finitely many purely pseudoanosov subgroups of a mapping class group that are isomorphic to a given one-ended finitely presented group.

#### Article information

**Dates**

Received: 31 January 2015

Revised: 6 November 2015

First available in Project Euclid:
4 October 2018

**Permanent link to this document**

https://projecteuclid.org/
euclid.aspm/1538671938

**Digital Object Identifier**

doi:10.2969/aspm/07310013

**Mathematical Reviews number (MathSciNet)**

MR3728491

#### Citation

Bowditch, Brian H. One-ended subgroups of mapping class groups. Hyperbolic Geometry and Geometric Group Theory, 13--36, Mathematical Society of Japan, Tokyo, Japan, 2017. doi:10.2969/aspm/07310013. https://projecteuclid.org/euclid.aspm/1538671938