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

Nestor Colin; Rita Jiménez Rolland; Porfirio L. León Álvarez; Luis Jorge Sánchez Saldaña

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arXiv · 2412.14410

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

Nestor Colin·Rita Jiménez Rolland·Porfirio L. León Álvarez·Luis Jorge Sánchez Saldaña

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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.

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Nestor Colin, Rita Jiménez Rolland, Porfirio L. León Álvarez, Luis Jorge Sánchez Saldaña. 2024-12-18. The proper geometric dimension of the mapping class group of an orientable surface with punctures. https://arxiv.org/abs/2412.14410

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