A spine for the decorated Teichm\"uller space of a punctured non-orientable surface
Geometric Topology
2025-04-09 v1 Algebraic Topology
Group Theory
Abstract
Building on work of Harer \cite{Ha86}, we construct a spine for the decorated Teichm\"uller space of a non-orientable surface with at least one puncture and negative Euler characteristic. We compute its dimension, and show that the deformation retraction onto this spine is equivariant with respect to the pure mapping class group of the non-orientable surface. As a consequence, we obtain a model for the classifying space for proper actions of the pure mapping class group of a punctured non-orientable surface, which is of minimal dimension in the case there is a single puncture.
Cite
@article{arxiv.2504.05404,
title = {A spine for the decorated Teichm\"uller space of a punctured non-orientable surface},
author = {Nestor Colin and Rita Jiménez Rolland and Porfirio L. León Álvarez and Luis Jorge Sánchez Saldaña},
journal= {arXiv preprint arXiv:2504.05404},
year = {2025}
}
Comments
15 pages, 5 figures