## Abstract

We give a criterion to prove that some groups are not acylindrically hyperbolic. As an application, we prove that the mapping class group of an infinite type surface is not acylindrically hyperbolic.

Show Summary Details# Big mapping class groups are not acylindrically hyperbolic

## Abstract

## References

## About the article

More options …# Mathematica Slovaca

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Editor-in-Chief: Pulmannová, Sylvia

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- Online
- ISSN
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Juliette Bavard / Anthony Genevois

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Get Access to Full TextWe give a criterion to prove that some groups are not acylindrically hyperbolic. As an application, we prove that the mapping class group of an infinite type surface is not acylindrically hyperbolic.

MSC 2010: Primary 20F65; Secondary 20F67

Keywords: mapping class groups; infinite type surfaces; acylindrically hyperbolic groups

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**Received**: 2016-01-31

**Accepted**: 2016-03-23

**Published Online**: 2018-02-09

**Published in Print**: 2018-02-23

**Citation Information: **Mathematica Slovaca, Volume 68, Issue 1, Pages 71–76, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0081.

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