The proper geometric dimension of the mapping class group
Javier Aramayona, Conchita Mart\'inez-P\'erez
TL;DR
This paper proves that the mapping class group of a closed surface has a cocompact classifying space for proper actions whose dimension matches its virtual cohomological dimension, clarifying its geometric properties.
Contribution
It establishes that the geometric dimension of the mapping class group equals its virtual cohomological dimension, providing a precise geometric understanding.
Findings
Dimension of the classifying space equals the virtual cohomological dimension.
The classifying space for proper actions is cocompact.
Clarifies the geometric structure 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.
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