Questions about algebraic methods and invariants to study and classify topological spaces: homotopy groups, (co)-homology groups, and beyond.

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5
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+150

Action of $\operatorname{Aut}(G)$ on the Borel construction

I am interested into the (say real) regular representation $\rho$ of $G=(\mathbb{Z}/p)^n$. Considering the universal vector bundle $EG\rightarrow BG$, the Borel construction with the regular ...
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+100

Is there a homology theory that counts connected components of a space?

It is well-known that the generators of the zeroth singular homology group $H_0(X)$ of a space $X$ correspond to the path components of $X$. I have recently learned that for Čech homology the ...