Timeline for homotopy type of embeddings versus diffeomorphisms
Current License: CC BY-SA 3.0
8 events
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| Jan 31, 2013 at 6:34 | comment | added | Ricardo Andrade | (continuation) Most of the details in my answer are spent setting up all the hypotheses for the induction, and checking that the procedure above can be performed continuously when $\varphi$ varies over a (compact) space. In any case, I do hope that you will let me know if you find any issues or have any comments regarding my answer or this question. I will truly appreciate it! | |
| Jan 31, 2013 at 6:28 | comment | added | Ricardo Andrade | @Tom: I hope the underlying argument is valid, even though I wrote it in a detailed manner not so conducive to intuition. The basic idea --- gleaned from Agol's answer --- is to take an isotopy $\varphi$ in the homotopy fibre, and use the isotopy extension lemma to inductively push the support of $\varphi$ outside of each stage of a suitable exhaustion of $M$ by compact submanifolds. This will converge to the constant identity isotopy because we are using the compact-open $C^1$ topology. (to be continued) | |
| Jan 31, 2013 at 1:02 | comment | added | Tom Goodwillie | I can't honestly say that I read your answer through all that carefully, although I plan to. I'd like to really understand this. | |
| Jan 30, 2013 at 12:41 | history | edited | Tom Goodwillie | CC BY-SA 3.0 |
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| Jan 28, 2013 at 13:07 | comment | added | Tom Goodwillie | Yes, I've rewritten it. | |
| Jan 25, 2013 at 3:42 | history | edited | Tom Goodwillie | CC BY-SA 3.0 |
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| Jan 23, 2013 at 6:08 | comment | added | Ricardo Andrade | Thank you very much, Tom. There is an interesting relation between your answer and Agol's answer to my previous question. Perhaps one can merge the two ideas (yours and Agol's) to do the open case? Seems hard... By the way, by "a swindle" do you mean "pushing off to infinity"? | |
| Jan 23, 2013 at 5:08 | history | answered | Tom Goodwillie | CC BY-SA 3.0 |