Homological stability of spin mapping class groups and quadratic symplectic groups
Abstract
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.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Algebraic structures and combinatorial models
Advanced Operator Algebra Research
Publication details
- Journal / source
- Forum of Mathematics Sigma
- Volume
- 14
- Publication date
- 1 January 2026
- Language
- EN