English

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

Geometric Topology 2024-12-20 v1 Group Theory

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 Mart\'inez P\'erez. As a consequence of our result we also obtain the proper geometric dimension of {\it full} spherical braid groups.

Keywords

Cite

@article{arxiv.2412.14410,
  title  = {The proper geometric dimension of the mapping class group of an orientable surface with punctures},
  author = {Nestor Colin and Rita Jiménez Rolland and Porfirio L. León Álvarez and Luis Jorge Sánchez Saldaña},
  journal= {arXiv preprint arXiv:2412.14410},
  year   = {2024}
}

Comments

17 pages. 11 tables