Sectional category of subgroup inclusions and sequential topological complexities of aspherical spaces as A-genus

Abstract

In this paper we characterize the sectional category of subgroup inclusions and the $r^{th}$-sequential topological complexity of aspherical spaces of a group G in terms of the A-genus in the sense of Clapp-Puppe and Bartsch for a suitable one-element family of G-spaces A, and we discuss some of the consequences of such characterization, including new ideas about notions of category-like invariants with respect to proper actions of groups.

Several additions and improvements, a gap in a proof filled. Preliminary version, all comments are welcomed!