Timeline for A possible generalization of the homotopy groups.
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 16, 2013 at 14:33 | comment | added | Alexander Chervov | arxiv.org/abs/math/9904026 Groups of Flagged Homotopies and Higher Gauge Theory Valery V.Dolotin - there is some generalization of the homotopy groups. | |
| Oct 4, 2010 at 9:57 | answer | added | Ronnie Brown | timeline score: 8 | |
| Sep 7, 2010 at 9:03 | answer | added | Mark Grant | timeline score: 27 | |
| Sep 6, 2010 at 20:56 | vote | accept | Daniel Miller | ||
| Sep 5, 2010 at 21:53 | comment | added | Daniel Moskovich | Mike- isn't this true even if we restricted to based maps for all based <i>co-Moore</i> spaces at once to X? Or am I completely off-base? | |
| Sep 5, 2010 at 20:39 | comment | added | Charles Staats | There's something similar to this that I thought of once: given any two spaces $X$ and $Y$, the set of homotopy classes of maps $X \times I \to Y$ sending all $(x, 0)$ and $(0,x)$ to a fixed base point form a group. If $X = I^{n-1}$, I believe the result contains, at least in some cases, all the homotopy groups $\pi_1$ through $\pi_n$. But given how hard the latter are to compute, I doubt that this construction is all that useful. [But if it is, I am not in a position to know.] | |
| Sep 5, 2010 at 20:20 | answer | added | Daniel Moskovich | timeline score: 12 | |
| Sep 5, 2010 at 17:25 | comment | added | Mike Shulman | Well, if you examine homotopy classes of based maps from all based spaces Y at once, then you get enough information to characterize the space X up to homotopy equivalence, by the Yoneda lemma in the homotopy category. (-: | |
| Sep 5, 2010 at 14:26 | answer | added | Charles Rezk | timeline score: 36 | |
| Sep 5, 2010 at 13:33 | history | asked | Daniel Miller | CC BY-SA 2.5 |