The proper geometric dimension of the mapping class group of an orientable surface with punctures
Abstract
We show that the full mapping class group of any orientable closed surface with punctures admits a cocompact classifying space for proper actions of dimension equal to its virtual cohomological dimension. This was proved for closed orientable surfaces and for pure mapping class groups by Aramayona and Mart\'inez P\'erez. As a consequence of our result we also obtain the proper geometric dimension of full spherical braid groups.
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