Homological stability for certain classical groups

TL;DR

This paper establishes homological stability for classical groups such as unitary and general linear groups over various fields, highlighting similarities and differences in the proofs based on prior work by Sah.

Contribution

It extends homological stability results to unitary and linear groups over different fields, comparing proof techniques and broadening understanding of these groups' algebraic topology.

Findings

Homological stability proven for unitary groups over R, C, H

Homological stability proven for general linear groups over skew-fields

Comparison of proof methods for different classical groups

Abstract

We prove homological stability for standard unitary groups over R, C and H and for general linear groups over skew-fields with infinite centre. We focus on the similarities and differences of these proofs. Both proofs are due to Chih-Han Sah (Homology of classical Lie groups made discrete I: Stability theorems and Schur multipliers. Comment. Math. Helv. 61(2), 1986).