Classifying spaces for proper actions of mapping class groups

TL;DR

This paper constructs a cocompact model for the classifying space for proper actions of mapping class groups of surfaces with punctures and boundaries, extending known models for closed surfaces through an inductive approach.

Contribution

It introduces a new cocompact model for the classifying space of mapping class groups of punctured and bordered surfaces, generalizing previous models for closed surfaces.

Findings

Provides a cocompact model for the classifying space for proper actions

Uses induction on punctures and boundary components

Extends known models for closed surfaces

Abstract

We describe a cocompact model for the classifying space for proper actions of the mapping class group of a surface with punctures and boundary components. Our construction relies on a known model for the case of a closed surface and uses an induction on the number of punctures and boundary components.