3
votes
1answer
169 views

Stable homotopy of classifying space for nilpotent groups

Let $BG$ denote the classifying space of a (discrete) group and $BG_+$ its disjoint union with a point. Question: What is known about the stable homotopy groups $\pi^S_*(BG_+)$ ? If $G$ is finite ...
1
vote
1answer
274 views

Homotopy classification of maps into nilmanifolds

I am interested in answers or reference in the literature to the following problem: Classify up to homotopy all maps $A\to X$, where $A$ is a closed oriented manifold and $X$ is a closed ...