Homological stability for symplectic groups via algebraic arc complexes
Abstract
We use algebraic arc complexes to prove a homological stability result for symplectic groups with slope 2 3 \frac {2}{3} for rings with finite unitary stable rank. Symplectic groups are here interpreted as the automorphism groups of formed spaces with boundary , which are algebraic analogues of surfaces with boundary, that we also study in the present paper. Our stabilization map is a rank one stabilization in the category of formed spaces with boundary, going through both odd and even symplectic groups.
Fields of Study & Subjects
Geometric and Algebraic Topology
Advanced Algebra and Geometry
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Transactions of the American Mathematical Society
- Volume
- 379
- Issue
- 9
- Pages
- 6613–6659
- Publication date
- 16 June 2026
- Language
- EN