We consider brave new cochain extensions F(BG +,R) → F(EG +,R), where R is either a Lubin-Tate spectrum E n or the related 2-periodic Morava K-theory K n, and G is a finite group. When R is an Eilenberg-Mac Lane spectrum, in some good cases such an extension is a G-Galois extension in the sense of John Rognes, but not always faithful. We prove that for E n and K n these extensions are always faithful in the K n local category. However, for a cyclic p-group $C_{p^r}$, the cochain extension $F(B{C}_{p^r+},E_n)\to F(E{C}_{p^r+},E_n)$ is not a Galois...

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(ν,A) to Gl(n,A), ν < n, A = ℤ, resp. ${\mathbb{Z}}_p$, does the image of f have infinite, resp. uncountably infinite, index in...