Isoperimetric inequalities for the handlebody groups

TL;DR

This paper establishes that the Dehn function of the handlebody group's mapping class group grows at most exponentially, providing insights into the group's geometric and algebraic properties.

Contribution

It proves an upper bound of exponential growth for the Dehn function of handlebody groups, a significant step in understanding their geometric complexity.

Findings

Dehn function of handlebody groups is at most exponential

Provides new bounds on the geometric complexity of handlebody groups

Advances understanding of the algebraic properties of handlebody groups

Abstract

We show that the mapping class group of a handlebody of genus at least 2 has a Dehn function of at most exponential growth type.