Genus sets and SNT sets of certain connective covering spaces
Volume 195 / 2007
Fundamenta Mathematicae 195 (2007), 135-153
MSC: 55P60, 55P62, 55P15, 20G99.
DOI: 10.4064/fm195-2-3
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 ${\rm Gl}(\nu, A)$ to ${\rm Gl}(n,A)$, $\nu < n$, $A=\mathbb{Z}$, resp. $\mathbb{Z}_p$, does the image of $f$ have infinite, resp. uncountably infinite, index in ${\rm Gl}(n,A)$?
