The class of loop spaces of which the mod $p$ cohomology is Noetherian is much larger than the class of $p$-compact groups (for which the mod $p$ cohomology is required to be finite). It contains Eilenberg–Mac Lane spaces such as $ℂP^{\infty }$ and 3-connected covers of compact Lie groups. We study the cohomology of the classifying space $BX$ of such an object and prove it is as small as expected, that is, comparable to that of $BℂP^{\infty }$. We also show that $B$X differs basically from the classifying space of a $p$-compact group...

In this article we study non-abelian extensions of a Lie group $G$ modeled on a locally convex space by a Lie group $N$. The equivalence classes of such extension are grouped into those corresponding to a class of so-called smooth outer actions $S$ of $G$ on $N$. If $S$ is given, we show that the corresponding set $\mathrm{Ext}{(G,N)}_S$ of extension classes is a principal homogeneous space of the locally smooth cohomology group $H_{ss}^2{(G,Z\left(N\right))}_S$. To each $S$ a locally smooth obstruction class $\chi \left(S\right)$ in a suitably defined cohomology group $H_{ss}^3{(G,Z\left(N\right))}_S$ is defined....