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arXiv · 2211.06219

Homological stability of spin mapping class groups and quadratic symplectic groups

Ismael Sierra
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Abstract

We study the homological stability of spin mapping class groups of surfaces and of quadratic symplectic groups using cellular $E_2$-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 $\mathbb{F}_2$-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.

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Ismael Sierra. 2022-11-11. Homological stability of spin mapping class groups and quadratic symplectic groups. https://doi.org/10.1017/fms.2025.10152

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