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In this article from 1990, Stover describes a specral sequence which converges to the higher homotopy groups of the homotopy colimit of a diagram $\underline{X}$ of topological spaces. The second ...

Let $f\colon X \rightarrow Y$ be a continuous map of sufficiently nice topological spaces (say, smooth manifolds). Let ${\cal F}=(\dots\rightarrow F_i \rightarrow F_{i+1}\to \dots)$ be a bounded ...

This question was asked on math.stackexchange and didn't receive any traction, so I'm turning to the MO community. Hello! Let $C_{\bullet}$ and $D_{\bullet}$ be chain complexes of $R$-modules for some ...

In "A primer on spectral sequences" http://www.math.uchicago.edu/~may/MISC/SpecSeqPrimer.pdf (by J.P.May apparently, although no name is given in the pdf) I found a very detailed version of the ...

Let $p\colon E\to B$ and $p'\colon E'\to B'$ be two fibrations. Assume for simplicity that $B,B'$ are simply connected. Let we have morphism of these fibrations, i.e. two continuous maps $$f\colon E\...

Related to the question here, here is another question. Consider the kernel of the map $H_*(QY;Z/p)\rightarrow H_{*+1}(Q\Sigma Y;Z/p)$. restricted to $PH_*(QY)$, and let's say $Y$ itself is a ...