On the virtually-cyclic dimension of mapping class groups of punctured spheres

TL;DR

This paper computes the virtually-cyclic dimension of mapping class groups for punctured spheres with up to six punctures, providing new insights into their algebraic and geometric properties.

Contribution

It determines the virtually-cyclic dimension for specific classes of mapping class groups, including punctured spheres, twice-holed tori, and genus-two surfaces.

Findings

Virtually-cyclic dimension of punctured spheres with up to six punctures calculated.

Virtually-cyclic dimension of twice-holed torus mapping class group obtained.

Virtually-cyclic dimension of genus-two surface mapping class group determined.

Abstract

We calculate the virtually-cyclic dimension of the mapping class group of a sphere with at most six punctures. As an immediate consequence, we obtain the virtually-cyclic dimension of the mapping class group of the twice-holed torus and of the closed genus-two surface.