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The proper geometric dimension of the mapping class groups of non-orientable surfaces with punctures

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

We study the proper geometric dimension of {\it full} mapping class groups of non-orientable surfaces with punctures. Building on the computation for closed non-orientable surfaces, we prove that the proper geometric dimension agrees with the virtual cohomological dimension in all but a finite collection of low-complexity cases, for which we obtain explicit bounds. Our results provide the non-orientable counterpart of the corresponding computations for mapping class groups of closed and punctured orientable surfaces.

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Cite

BibTeXRIS
BibTeX
@misc{colin2026proper,
  title = {{The proper geometric dimension of the mapping class groups of non-orientable surfaces with punctures}},
  author = {Nestor Colin and Rita Jiménez Rolland and Porfirio L. León Álvarez and Luis Jorge Sánchez Saldaña},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.22505},
  eprint = {2609.22505},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22505},
}
RIS
TY  - UNPB
TI  - The proper geometric dimension of the mapping class groups of non-orientable surfaces with punctures
AU  - Nestor Colin
AU  - Rita Jiménez Rolland
AU  - Porfirio L. León Álvarez
AU  - Luis Jorge Sánchez Saldaña
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.22505
UR  - https://arxiv.org/abs/2609.22505
AB  - We study the proper geometric dimension of {\it full} mapping class groups of non-orientable surfaces with punctures. Building on the computation for closed non-orientable surfaces, we prove that the proper geometric dimension agrees with the virtual cohomological dimension in all but a finite collection of low-complexity cases, for which we obtain explicit bounds. Our results provide the non-orientable counterpart of the corresponding computations for mapping class groups of closed and punctured orientable surfaces.
ER  -