Homological stability of spin mapping class groups and quadratic symplectic groups

2022/11/11 by Sierra, Ismael · 1 citation
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.06219

Abstract

We study the homological stability of spin mapping class groups of surfaces and of quadratic symplectic groups using cellular E₂-algebras. We get improvements in their stability results, which for the spin mapping class groups we show to be optimal away from the prime 2. We also prove that in both cases the \mathbbF₂-homology satisfies secondary homological stability. Finally, we give full descriptions of the first homology groups of the spin mapping class groups and of the quadratic symplectic groups.

Cited by

• Modular representations via the first homology of congruence subgroups of mapping class groups and automorphism groups of free groups

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• Mod 2 homology of the stable spin mapping class group
• Secondary homological stability for mapping class groups of nonorientable surfaces
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• Symplectic Groups, Mapping Class Groups and the Stability of Bounded Cohomology