Secondary homological stability for mapping class groups of nonorientable surfaces

2021/12/24 by Max Vistrup, Vistrup, Max
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2112.13084

openalex publication_date 2021/12/24 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

Using the Galatius--Kupers--Randal-Williams framework of cellular E₂-algebras, we prove a secondary stability theorem for mapping class groups of nonorientable surfaces. As a corollary, we obtain a new best known stability range for the homology of the mapping class groups of nonorientable surfaces with respect to adding torus holes.

Related

• Homological stability of non-orientable mapping class groups with marked points
• Improved homological stability for the mapping class group with integral or twisted coefficients
• Homological stability of spin mapping class groups and quadratic symplectic groups
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• Secondary representation stability and the ordered configuration space of the once-punctured torus