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May
15
comment References for equivariant cohomology
You could start with the "What is... equivariant cohomology?" article from the Notices of the AMS. Then I heard there is a book by Bredon on the subject.
May
1
comment Curious remark of D. Ravenel
This article is incredibly funny.
Apr
30
comment If there are injective homomorphisms between two groups in both directions, are they isomorphic?
See also mathoverflow.net/questions/1058/when-does-cantor-bernstein-hold
Apr
16
comment What are some beautiful examples of adjunctions?
math.stackexchange.com/questions/46708/…
Apr
8
comment Why are functors exact if they preserve all short exact sequences?
At the end of this answer to a related question, I post a link to something I wrote up (in Spanish) which contains exactly what you want. If you understand it and write it up in English and post it as an answer, I'd upvote it :)
Apr
6
comment Classification of finitely generated multigraded modules over $K[x_1,\ldots,x_n]$?
Why the hell does this have a -3 vote count? (-2 now). Sometimes I really don't understand math.SE user's vote patterns.
Apr
6
comment Ring structure on $Ext$ and $Tor$
Found another reference: Mac Lane's Homology, section VIII (Products). There's also Cartan & Eilenberg which is really comprehensive and immensely general. And I'm going to leave a link to a question I just asked here, because it is somehow related and I think it would be useful to have them formally linked: math.stackexchange.com/questions/1222604/… .
Apr
6
comment Reference request: extending tensor product of modules
Do you want a reference where it is used (it's used all over the place!), as you say, or do you want a reference where it is explained? If it's the latter, try KConrad's two blurbs on tensor products, they are very nice. It's called "extension of scalars" or "base change", usually.
Mar
31
comment Explicit example of Koszul complex
Do you have a reference for the content of your post? Thanks.
Mar
31
comment How to compute Ext over an exterior algebra
Also, this question is definitely related, if not almost a duplicate: math.stackexchange.com/questions/366927/…
Mar
30
comment How to compute Ext over an exterior algebra
You should look at Lang's Algebra, almost at the end of the book: it's p. 861 in my edition.
Mar
29
comment Ring structure on $Ext$ and $Tor$
You should check these notes by May: math.uchicago.edu/~may/MISC/TorExt.pdf
Mar
11
comment Why the whole exterior algebra?
I am tempted to give the following application: exterior algebras are important because they are particular cases of Clifford algebras which are important in full, not just their homogeneous coordinates, for example in constructing the Atiyah-Bott-Shapiro isomorphism (aka algebraic Bott periodicity). But I'm not comfortable enough with these concepts to post this as an answer, and it is stretching it a bit (ABS theorem does not consider trivial Clifford algebras, i.e. exterior algebras).
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
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
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
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.