On the Homology stability range for symplectic groups
K-Theory and Homology
2026-01-14 v1 Algebraic Topology
Abstract
We improve, by a factor of 2, known homology stability ranges for the integral homology of symplectic groups over commutative local rings with infinite residue field and show that the obstruction to further stability is bounded below by Milnor-Witt K-theory. In particular our stability range is optimal in many cases.
Cite
@article{arxiv.2205.08021,
title = {On the Homology stability range for symplectic groups},
author = {Marco Schlichting},
journal= {arXiv preprint arXiv:2205.08021},
year = {2026}
}