Homological stability: a tool for computations

TL;DR

This paper reviews tools and techniques for proving homological stability theorems and computing stable homology, demonstrating their application through the example of Higman-Thompson groups.

Contribution

It provides a survey of methods for establishing homological stability and computes the stable homology for Higman-Thompson groups, illustrating the approach.

Findings

Homological stability is effective for computing homology of various groups.

The paper demonstrates the computation of stable homology for Higman-Thompson groups.

Tools and techniques for homological stability are systematically surveyed.

Abstract

Homological stability has shown itself to be a powerful tool for the computation of homology of families of groups such as general linear groups, mapping class groups or automorphisms of free groups. We survey here tools and techniques for proving homological stability theorems and for computing the stable homology, and illustrate the method through the computation of the homology of Higman-Thompson groups.