Homological stability for symplectic groups via algebraic arc complexes
Algebraic Topology
2025-11-07 v2
Abstract
We use algebraic arc complexes to prove a homological stability result for symplectic groups with slope 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.
Cite
@article{arxiv.2411.07895,
title = {Homological stability for symplectic groups via algebraic arc complexes},
author = {Ismael Sierra and Nathalie Wahl},
journal= {arXiv preprint arXiv:2411.07895},
year = {2025}
}
Comments
Various improvements following referee reports, including a new remark 2.20 about monoidal structures. Final version, to appear in Trans. AMS