Timeline for When are maps between topological spaces homotopic?
Current License: CC BY-SA 3.0
21 events
| when toggle format | what | by | license | comment | |
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| Jul 19, 2013 at 21:13 | comment | added | Tom Goodwillie | But I think I caught him on a good day. He had a reputation for not suffering fools gladly, but he was quite gentle on that occasion. | |
| Jul 19, 2013 at 21:12 | comment | added | Tom Goodwillie | I once briefly made this same error--mistaking Whitehead's Theorem for that much stronger and false statement. 37 years later the memory still makes me cringe, and this is partly because the person who corrected my misconception was none other than the late Frank Adams. | |
| Jul 19, 2013 at 10:13 | answer | added | Ronnie Brown | timeline score: 5 | |
| Jul 18, 2013 at 19:01 | comment | added | Johannes Ebert | @Kofi: no, Whiteheads theorem can almost never be used to prove that two maps are homotopic. | |
| Jul 18, 2013 at 16:22 | comment | added | Todd Trimble | Thanks, Oscar -- you're right. Naively what I was trying to do was consider a homotopy equalizer. Oh well. | |
| Jul 18, 2013 at 16:03 | history | edited | Vidit Nanda |
added tag
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| Jul 18, 2013 at 15:56 | comment | added | David E Speyer | An old question of mine seems relevant: mathoverflow.net/questions/2672/whitehead-for-maps | |
| Jul 18, 2013 at 15:45 | answer | added | Vidit Nanda | timeline score: 3 | |
| Jul 18, 2013 at 15:08 | comment | added | Oscar Randal-Williams | @Todd: the homotopy fibre of $P \to X$ is equivalent to the loop space $\Omega Y$, so $P \to X$ will rarely induce an isomorphism on homotopy groups. | |
| Jul 18, 2013 at 14:39 | comment | added | Marc Palm | Thanks Todd for that interpretation, but I didn't really think that far when closing. | |
| Jul 18, 2013 at 14:36 | history | edited | Todd Trimble | CC BY-SA 3.0 |
added some LaTeX
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| Jul 18, 2013 at 14:35 | comment | added | Todd Trimble | Well, I thought Marc meant it can be deduced from Whitehead's theorem. It seems to me one might consider the pullback $P$ of $\langle f, g \rangle: X \to Y \times Y$ along the path fibration $Y^I \to Y \times Y$ and show that the projection $P \to X$ induces an isomorphism on all homotopy groups, and then apply Whitehead. | |
| Jul 18, 2013 at 14:33 | comment | added | Matthias Ludewig | So for connected CW-complexes, by Whiteheads theorem, you get that the homotopy classes are classified by the maps between the corresponding homotopy groups. | |
| Jul 18, 2013 at 14:33 | comment | added | Marc Palm | I retracted my close vote. | |
| Jul 18, 2013 at 14:32 | comment | added | Marc Palm | Sorry, I misread your question. You are of course right. | |
| Jul 18, 2013 at 14:30 | answer | added | Mark Grant | timeline score: 6 | |
| Jul 18, 2013 at 14:15 | comment | added | quiver | No this isn't Withehead's theorem. Whitehead's theorem says that if a map induces an isomorphism on all homotopy groups then it is a homotopy equivalence. | |
| Jul 18, 2013 at 14:08 | review | Close votes | |||
| Jul 18, 2013 at 16:21 | |||||
| Jul 18, 2013 at 13:58 | review | First posts | |||
| Jul 18, 2013 at 14:37 | |||||
| Jul 18, 2013 at 13:49 | comment | added | Marc Palm | I voted to close, because it is wellknown: en.wikipedia.org/wiki/Whitehead_theorem | |
| Jul 18, 2013 at 13:41 | history | asked | quiver | CC BY-SA 3.0 |