User talk:Jakob.scholbach/Archives/2007/November

Homotopy groups of spheres

I fear my attempts to define our goals at Talk:Homotopy groups of spheres#Impossible dream may have offended you. That was not at all my intent, and I do hope you will continue to contribute. --KSmrq^T 22:40, 2 November 2007 (UTC)

OK, I see. I was indeed offended, but I will not be resentful any longer. (As an aside: Gandhi in his autobiography writes "Hate the sin, but not the sinner". It is sometimes difficult, but I often made good experiences separating the deeds etc. of a person and the person itself). Concerning the homotopy groups of spheres, I will try to incorporate some of the material of the draft into the homotopy groups and possibly the functor articles. Regards, Jakob.scholbach 12:56, 3 November 2007 (UTC)

Great!

Wikipedia can be an endless time sink because of all the links. I'll start to fix one little thing, follow a link to discover a supporting article in really horrible shape, spend a little time correcting the most visible problems, and on and on and on. Often now I force myself not to stop and fix problems I see, because I'd never get the primary task finished. If you want to devote a little time to polishing some of the articles this one draws from, that could indeed be a good place for the material.

As for the Definitions (now "Background") section, we are facing a familiar challenge. If we leave all the background to other articles we can quickly focus on the discussion of the title topic, but sometimes just a sentence or two can fill in enough so that readers don't have to chase a dozen links to get oriented. I believe Geometry guy wanted to try polishing this article precisely because it demands more background, to see how well we can handle the challenge. As you well know, most of advanced mathematics carries the same burden. A fun and practical rule of thumb I heard from some graduate students concerned colloquia: if you could understand two consecutive words of the title it might be worth attending. :-) --KSmrq^T 16:17, 3 November 2007 (UTC)

Homology of groups

Howdy, thanks for adding a section on homology of groups to Group cohomology. It was badly needed and had been on my todo list for quite some time, but I had yet to feel like starting from scratch. Now it was easy to add a few things, and should make it easier to write the "low degree interpretations" section that is in every textbook.

Can you check the new citation for consistency? I've used the {{cite}} template before, but not the {{citation}} or Harvard citations/anti-footnotes. JackSchmidt 20:56, 6 November 2007 (UTC)

Hi, wow, that was an express extension! Well, I think your definition is one of the standard ones, which are all equivalent. The citation is fine. Some advocate the use of ISBN 13, but that's not a big deal, I think. (I've written a database which is supposed to facilitate referencing, see zeteo.info). I think we should make a separate article once it gets some more material. (Another stab - I don't know if you know that already: lots of mathematical notation can be done without resorting to <math>...</math>, there are equivalents for lots of symbols, see User:KSmrq/Chars). Happy editing! Jakob.scholbach 21:21, 6 November 2007 (UTC)

I fixed the isbn13. The non <math></math> version of Tor looks pretty good, but I've had Unicode versions converted to math tags a lot and so usually don't bother on articles already using the math tags. Here is the version I made, do you think the Tor^ZG part looks funny?

The functor which assigns M_G to M is isomorphic to the functor which sends M to ℤ ⊗_ℤ[G] M, where ℤ is endowed with the trivial G-action. Hence one also gets an expression for group homology in terms of the Tor functors, H_n(G, M) = Tor_n^ℤ[G](ℤ,M).

JackSchmidt 21:42, 6 November 2007 (UTC)

Yes, you're right. Often it is not really good. Let's hope some day they will fix this oddity... Jakob.scholbach 21:49, 6 November 2007 (UTC)