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The proper geometric dimension of the mapping class group

Javier Aramayona, Conchita Martínez-Pérez

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.

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.

Paper Structure

This paper contains 6 sections, 9 theorems, 25 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Virtual cohomological dimension
  4. Riemann-Hurwitz formula
  5. Preliminaries on classifying spaces for proper actions
  6. Proof of Theorem \ref{['main']}

Key Result

Theorem 1.1

For any $g\ge 0$ there exists a cocompact $\underline{\rm{E}} \Gamma_{g,0}$ of dimension equal to $\operatorname{vcd}(\Gamma_{g,0})$. In other words, $\underline{\rm{gd}}(\Gamma_{g,0}) = \operatorname{vcd}(\Gamma_{g,0})$.

Theorems & Definitions (20)

  • Theorem 1.1
  • Theorem 1.2: luck
  • Corollary 1.3
  • Remark 1.4
  • Theorem 2.1: Harer
  • Remark 2.2
  • Lemma 2.3
  • proof
  • Remark 3.1
  • Definition 3.2: Length
  • ...and 10 more