Genus sets and SNT sets of certain connective covering spaces

Abstract

We study the genus and SNT sets of connective covering spaces of familiar finite CW-complexes, both of rationally elliptic type (e.g. quaternionic projective spaces) and of rationally hyperbolic type (e.g. one-point union of a pair of spheres). In connection with the latter situation, we are led to an independently interesting question in group theory: if f is a homomorphism from Gl(�,A) to Gl(n,A), � < n, A = Z, resp. Zp, does the image of f have infinite, resp. uncountably infinite, index in Gl(n,A)? 1. Introduction and statement of results. In this paper, we study the genus sets and SNT sets of certain m-connective covering spaces Xh mi , following the work initiated by McGibbon and Moller ((16)), and continued by McGibbon and Roitberg ((17)). Before stating our main results, we recall the basic notions; in the following definitions, X and Y are assumed to be spaces of the homotopy type of nilpotent, finite type CW-complexes.