On classifying spaces for the family of virtually cyclic subgroups in mapping class groups

TL;DR

This paper establishes an upper bound on the geometric dimension for the family of virtually cyclic subgroups within mapping class groups of certain surfaces, advancing understanding of their algebraic and geometric properties.

Contribution

It provides a new bound for the geometric dimension of virtually cyclic subgroups in mapping class groups of punctured surfaces with boundary.

Findings

Bound for the geometric dimension established

Applicable to surfaces with punctures and boundary

Enhances understanding of mapping class group structures

Abstract

We give a bound for the geometric dimension for the family of virtually cyclic groups in mapping class groups of a compact surface with punctures, possibly with nonempty boundary and negative Euler characteristic.