Timeline for A homotopy commutative diagram that cannot be strictified
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Dec 14, 2011 at 7:10 | comment | added | Matthias Künzer | On the other hand, for which categories I is Top^I -> Ho(Top)^I dense? I.e. what is the condition on I that ensures that there is never an obstruction against rectifying a diagram of shape I? Cf. also mathoverflow.net/questions/39431/… . | |
| Dec 8, 2011 at 11:49 | answer | added | Jesper Grodal | timeline score: 14 | |
| Dec 3, 2011 at 4:17 | vote | accept | Akhil Mathew | ||
| Dec 2, 2011 at 22:43 | answer | added | Jeff Smith | timeline score: 19 | |
| Nov 26, 2011 at 20:05 | answer | added | Tom Goodwillie | timeline score: 18 | |
| Nov 26, 2011 at 16:14 | history | edited | Akhil Mathew | CC BY-SA 3.0 |
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| Nov 24, 2011 at 1:01 | answer | added | Dylan Wilson | timeline score: 10 | |
| Nov 23, 2011 at 22:14 | comment | added | Tom Goodwillie | A naturally occurring example of a functor $\mathcal I\to Ho(Top)$ is the one where $\mathcal I$ is the category of abelian groups and the functor takes $G$ to a Moore space: a simply connected space whose only nontrivial homology group is $H_n\cong G$ for some fixed $n\ge 2$. People have studied the obstructions to strictifying this. There are probably pretty small diagrams of abelian groups for which it can't be done. Google "equivariant Moore space". | |
| Nov 23, 2011 at 20:02 | answer | added | Tyler Lawson | timeline score: 12 | |
| Nov 23, 2011 at 19:28 | comment | added | Clark Barwick | The obstructions to which you allude in your first paragraph are introduced in Dwyer-Kan, "Realizing diagrams in the homotopy category by means of diagrams of simplicial sets," MR0744648, and "An obstruction theory for diagrams of simplicial sets," MR0749527. Your example can be adapted in the following way: any H-space that is not an A_n-space defines a functor $\Delta_{\leq n}\to\mathrm{Ho}\mathcal{S}$ that cannot be rectified. | |
| Nov 23, 2011 at 17:30 | comment | added | Oscar Randal-Williams | See the discussion starting on p.401 of: Cooke, George Replacing homotopy actions by topological actions. Trans. Amer. Math. Soc. 237 (1978), 391–406. | |
| Nov 23, 2011 at 17:16 | history | asked | Akhil Mathew | CC BY-SA 3.0 |