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Jan
15
comment Computing $\pi_4(S^3)$ using Serre spectral sequence
Ok, it's clear for the first question. For the second one, I think I got it assuming that the homology groups of $X$ are finitely generated. Which is true if its homotopy groups are f.g. (Serre classes). But its homotopy groups are those of spheres, which are f.g. because their homology groups are f.g. (Serre classes).
Jan
14
comment Simply connected reduced suspension on path connected X
Well, this doesn't say why $\pi_0(\Sigma X)=0$ :) (which can be seen just from the definition of $\Sigma X$).
Jan
14
revised Computing $\pi_4(S^3)$ using Serre spectral sequence
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Jan
13
comment Computing $\pi_4(S^3)$ using Serre spectral sequence
Thanks a lot for your answer. I will check the details tomorrow. I think I see it for the first question. As for the second one, it's odd that you use those results, because in Davis & Kirk's book it comes after the computation that $\pi_4(S^3)=\mathbb Z/2$...
Jan
13
comment Computing $\pi_4(S^3)$ using Serre spectral sequence
Care to explain the downvote? I'd be happy to improve the question.
Jan
13
asked Computing $\pi_4(S^3)$ using Serre spectral sequence
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comment What are some important examples of differential objects that aren't naturally graded?
I agree with Qiaochu's comment, however I think that it just hides the indices away in the category $\Delta$ which is defined combinatorially.
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comment Quasi-isomorphism from “almost acyclic” complex to its homology
In fact, what does "$X$ is quasi-isomorphic to $Y$" mean?
Sep
8
answered History of category theory
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