On the dimension of the mapping class groups of a non-orientable surface

2020/07/24 by Cristhian E. Hidber, Hidber, Cristhian E., Luis Jorge Sánchez Saldaña +3
Mathematics · #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2007.12542

openalex publication_date 2020/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let N_g be the mapping class group of a non-orientable closed surface. We prove that the proper cohomological dimension, the proper geometric dimension, and the virtual cohomological dimension of N_g are equal whenever g≠ 4,5. In particular, there exists a model for the classifying space of N_g for proper actions of dimension vcd(N_g)=2g-5. Similar results are obtained for the mapping class group of a non-orientable surface with boundaries and possibly punctures, and for the pure mapping class group of a non-orientable surface with punctures and without boundaries.

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