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Mar
11
comment Why the whole exterior algebra?
I sympathize with your answer, which is the same thing I thought when I read the question, but that still doesn't say why it would be useful to consider the whole graded algebra and not just its homogeneous components separately...
Mar
11
comment Is There a de Rham Homology
See mathoverflow.net/questions/16657/de-rham-homology
Mar
9
answered Spin structures, frame bundles, and trivializations over the 2-skeleton
Feb
26
awarded  Tumbleweed
Feb
19
revised Obstruction theory for homotopies
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Feb
19
asked Obstruction theory for homotopies
Feb
5
awarded  Nice Question
Jan
28
accepted Computing $\pi_4(S^3)$ using Serre spectral sequence
Jan
28
answered Computing $\pi_4(S^3)$ using Serre spectral sequence
Jan
27
comment Ring structure in the Serre spectral sequence
For what it's worth, I had the exact same problem, googled it and ended up here. I've been thinking about this on and off for some days, sometimes I think I've convinced myself that it's true, but then I realize it's not the case...
Jan
25
awarded  Nice Question
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
Jan
12
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Jan
9
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Dec
21
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