Timeline for Loopspace of an Eilenberg Maclane space K(G,n)
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 1, 2010 at 7:33 | comment | added | Andrew Stacey | (ctd) (Gosh, this is getting a bit long!). Defining K(G,n) as a space with certain homotopy groups makes me want to ask "So what?"! Why should I be interested in K(G,n) except as an exercise with which to torture algebraic topology students? But that it represents cohomology, ah, now that's something worth knowing! But then I've never taught algebraic topology and my head is full of cohomology operations, so I'm naturally inclined to that view and if I ever actually had to explain it all (in more than 2000 characters), I'm sure I'd end up agreeing with you! | |
| Oct 1, 2010 at 7:30 | comment | added | Andrew Stacey | (ctd) Again, had I been first on the scene I'd've asked for that clarification. The lack of article ("a K(G,n)" or "the K(G,n)") means that there are no clues either. So I would say that both of our answers can be summarised as: "If you actually define K(G,n) (rather than just having a vague notion of what it is), and then the rest is (fairly) automatic.". And so to the definitions. I find myself preferring to define something by what it does rather than what it is. So I'd rather that it was the simplicity of the homotopy groups of K(G,n) that came as a miraculous surprise. (ctd) | |
| Oct 1, 2010 at 7:27 | comment | added | Andrew Stacey | In so far as the first paragraph refers to me, had I come across this without any answers then I probably would have voted to close. But given that there were already answers, closing would have left those there and (as I said) I didn't like them. Also, in my own subject area, I feel less able to judge what should or shouldn't be closed because (as I hinted), I'm so far in that I don't really know where the boundary is. On to the mathematics. The question isn't really clear enough (which is what I was trying to get at) in that it doesn't explain what the questioner thinks K(G,n) is (ctd) | |
| Sep 30, 2010 at 20:53 | vote | accept | Sam | ||
| Sep 30, 2010 at 20:53 | |||||
| Sep 30, 2010 at 12:40 | history | answered | Allen Hatcher | CC BY-SA 2.5 |