On homological stability for orthogonal groups and special orthogonal groups

TL;DR

This paper investigates the homological stability of orthogonal and special orthogonal groups, providing calculations and structural insights into their homology under specific conditions.

Contribution

It offers new calculations of homological stability for these groups and explores their homology structure, including twisted coefficient cases.

Findings

Homological stability for special orthogonal groups established.

Stability results for orthogonal groups with twisted coefficients obtained.

Structural properties of the homology groups analyzed.

Abstract

The problem of homological stability helps us to catch the structure of group homology. We calculate homological stability of special orthogonal groups, and we also calculate the stability of orthogonal groups with determinant-twisted coefficients under a certain good situation. We also get some results about the structure of these homology.