The proper geometric dimension of the mapping class group

Abstract

We show that the mapping class group of a closed surface admits a cocompact classifying space for proper actions of dimension equal to its virtual cohomological dimension.

In the published version of this article, one of the two arguments we gave for Corollary 1.3 made an incorrect use of Harer's spine, which is in fact only valid for $n=1$. In this version, which supersedes the published version, we have included only the other argument, embedded in the paragraph before Corollary 1.3

References in corpus (2)

• Classifying spaces for proper actions of mapping class groups
• Well-rounded equivariant deformation retracts of Teichmüller spaces

Cited by in corpus (9)

• Dimension invariants for groups admitting a cocompact model for proper actions
• On classifying spaces for the family of virtually cyclic subgroups in mapping class groups
• Stable finiteness properties of infinite discrete groups
• Geometric dimension of lattices in classical simple Lie groups
• Hierarchically cocompact classifying spaces for mapping class groups of surfaces
• On the virtually-cyclic dimension of mapping class groups of punctured spheres
• Classifying spaces for the family of virtually cyclic subgroups of braid groups
• Dimension invariants of outer automorphism groups
• On the dimension of groups that satisfy certain conditions on their finite subgroups