# Questions tagged [spectral-sequences]

Spectral sequences compute homology groups by taking a sequence of approximations, and generalise exact sequences. They find application in algebraic topology.

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### Cohomology of the pullback of a fiber bundle over the torus (generalised Eilenberg-Moore spectral sequence?)

I've found myself in the following situation and the tools that have been suggested to me to calculate the necessary invariants don't quite seem up to the job (I may be wrong in this as I have very ...
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### “Cut-off” of the Adams exact couple in A. Hatcher's “Spectral Sequences in Algebraic Topology”

I have been reading Chapter 2. of A. Hatcher's "Spectral Sequences in Algebraic Topology", which is freely available at the author's website. I have trouble understanding the Adams exact couple, ...
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### filtered modules (LNAT, Davis & Kirk)

In Lecture Notes in Algebraic Topology by Davis & Kirk, on page 240, there is written: Q1: Is convergence of the filtration assumed in the first underline? Otherwise $\forall p: F_p=A$ is a ...
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### A spectral sequence for Tor

Suppose $R \to T$ is a ring map such that $T$ is flat as an $R$-module. Then for $A$ an $R$-module, $C$ a $T$-module there is an isomorphism \text{Tor}^R_n(A,C) \simeq \text{Tor}^T_n(A \otimes_R T,...
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### Is there a nice list of spectral sequences that don't come from particular constructions?

When you first learn about rings, it's important to have examples of, say, a PID which is not a Euclidean domain, a UFD which is not a PID, and so forth, to help build intuition and provide test cases....