The proper geometric dimension of the mapping class group of an orientable surface with punctures

Abstract

We show that the {\it 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 {\it pure} mapping class groups by Aramayona and Martínez Pérez. As a consequence of our result we also obtain the proper geometric dimension of {\it full} spherical braid groups.

17 pages. 11 tables