Resonance of basis-conjugating automorphism groups

TL;DR

This paper investigates the structure of the first resonance variety in the cohomology ring of basis-conjugating automorphism groups of free groups, providing new insights into their algebraic properties.

Contribution

It precisely characterizes the first resonance variety for automorphism groups acting by conjugation on free groups, a novel result in this area.

Findings

Determined the structure of the first resonance variety.

Provided explicit descriptions of the cohomology ring.

Enhanced understanding of automorphism groups of free groups.

Abstract

We determine the structure of the first resonance variety of the cohomology ring of the group of automorphisms of a finitely generated free group which act by conjugation on a given basis.