On the sectional category of subgroup inclusions and Adamson cohomology theory

TL;DR

This paper extends the concept of sectional category to subgroup inclusions using Adamson cohomology, generalizing topological complexity results for aspherical spaces.

Contribution

It introduces a new framework connecting subgroup inclusion sectional categories with Adamson cohomology, broadening the understanding of topological complexity.

Findings

Extended the characterization of topological complexity to subgroup inclusions

Linked sectional category with Adamson cohomology theory

Provided new insights into aspherical spaces and their invariants

Abstract

The sectional category of a subgroup inclusion $H \hookrightarrow G$ can be defined as the sectional category of the corresponding map between Eilenberg--MacLane spaces. We extend a characterization of topological complexity of aspherical spaces given by Farber, Grant, Lupton and Oprea to the context of sectional category of subgroup inclusions and investigate it by means of Adamson cohomology theory.