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Jun
23
comment Any compact embedded $2$-dimensional hypersurface in $\mathbb R^3$ has a point of positive Gaussian curvature
@Dtseng: true, thank you. I've corrected it. Some months after I wrote this answer I wrote it up in all formality here (in Spanish).
Jun
7
comment Homology of a co-h-space manifold
Corollary 13.66 in Switzer's book proves that for any cohomology theory with products, the product is trivial on a suspension. Maybe you can generalize his proof to co-h-spaces.
Jun
3
comment Characterizations of the $p$-Prüfer group
More than four years later, I should edit that seventh item to change those inclusions to "multiply by $p$" maps, but I don't want to bump the question to the front page.
Jun
3
comment Clarify: “$S^0$, $S^1$ and $S^3$ are the only spheres which are also groups”
The point is that the operation gotten from such a set-theoretical bijection has no reason to respect the topological/differentiable structure of $S^k$ in any way. So what they mean is, a group structure in $S^k$ that behaves well with respect to the topology/geometry. (Hence the Lie groups appearing in the answer below).
May
29
comment Why is the cartesian product so categorically robust?
This reminds me of this answer: math.stackexchange.com/a/25460/2614
May
29
comment Is there an analogue of Eilenberg-Maclane spaces for homology?
This is essentially this MO question: mathoverflow.net/questions/1438/… , and Mike's accurate answer & comment are essentially Tyler's.
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...