Timeline for Neighborhoods of the identity in diffeomorphism groups
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Sep 25, 2023 at 0:32 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
Links all round!
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| Mar 31, 2015 at 23:08 | vote | accept | Yuri M. | ||
| Mar 25, 2015 at 8:38 | comment | added | Peter Michor | You also need that the right invariant metric is geodesically complete (the geodesic equation is globally well-posed). | |
| Mar 24, 2015 at 23:44 | comment | added | Yuri M. | Correct me if I'm wrong, but this new argument seems to work whenever there is a right-invariant metric such that the exponential map is a local diffeomorphism, provided that $V$ is small enough to be a diffeomorphic image of an open ball under exp. I gather this is not known for $Diff_c(R^n)$ but is for Diff(S^1) with the $H^k$ metrics, when k is at least 1? | |
| Mar 13, 2015 at 20:40 | history | edited | Peter Michor | CC BY-SA 3.0 |
typo corrected
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| Mar 13, 2015 at 10:02 | history | edited | Peter Michor | CC BY-SA 3.0 |
deleted 34 characters in body
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| Mar 13, 2015 at 9:53 | history | edited | Peter Michor | CC BY-SA 3.0 |
added 2293 characters in body
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| Mar 12, 2015 at 23:49 | comment | added | Yuri M. | Thanks! although I'm not sure how simplicity might help here (?) Here's a different way to think of the same kind of question with a more metric formulation: put your favorite (complete, left-invariant) metric on Diff_c(M). Is there k so that every diffeomorphism in the epsilon ball about the identity is the product of k elements in the epsilon/2 ball? | |
| Mar 12, 2015 at 18:34 | history | answered | Peter Michor | CC BY-SA 3.0 |