Homological stability of spin mapping class groups and quadratic symplectic groups

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.

This new version just fixes some minor typos

References in corpus (3)

• Homology of the moduli spaces and mapping class groups of framed, r-Spin and Pin surfaces
• Spherical complexes attached to symplectic lattices
• The Picard group of the moduli space of r-Spin Riemann surfaces