Topological complexity of basis-conjugating automorphism groups

TL;DR

This paper calculates the topological complexity of specific Eilenberg-Mac Lane spaces linked to automorphism groups of free groups that act by conjugation, providing insights into their algebraic and topological structure.

Contribution

It introduces the computation of topological complexity for these automorphism groups and their subgroups, expanding understanding of their topological properties.

Findings

Topological complexity values for these automorphism groups are determined.

Results reveal new connections between algebraic automorphism groups and topological invariants.

Provides a framework for analyzing similar groups in topological and algebraic contexts.

Abstract

We compute the topological complexity of Eilenberg-Mac Lane spaces associated to the group of automorphisms of a finitely generated free group which act by conjugation on a given basis, and to certain subgroups.