Big mapping class groups are not acylindrically hyperbolic

TL;DR

This paper introduces a criterion to determine when groups are not acylindrically hyperbolic and applies it to show that the mapping class group of an infinite type surface lacks this property.

Contribution

The paper provides a new criterion for non-acylindrical hyperbolicity and demonstrates its use on infinite type surface mapping class groups.

Findings

Infinite type surface mapping class groups are not acylindrically hyperbolic.

The criterion effectively distinguishes groups that are not acylindrically hyperbolic.

Application of the criterion broadens understanding of group actions on infinite-type surfaces.

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.