Timeline for When is a bi-Lipschitz homeomorphism smoothable?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 23, 2020 at 3:03 | comment | added | Piotr Hajlasz | I am sorry, I was stupid. Exotic spheres are bi-Lipschitz homeomorphic exactly for a reason I mentioned: uniqueness of a Lipschitz structure. | |
| Sep 23, 2020 at 1:59 | comment | added | Igor Belegradek | @PiotrHajlasz: I do not claim to understand Luukkainen's paper, but I think what I say is a formal consequence of his Lemma 2.4 for $A=\emptyset$ and $B=M$. | |
| Sep 23, 2020 at 1:39 | comment | added | Piotr Hajlasz | I am not sure if the answer is correct. The link shows a self-homeomorphis, that is not isotopic to a diffeomorphism. This is because the manifold with reversed orientation are not diffeomorphic. I think the homeomorphism cannot be bi-Lipschitz due to uniqueness of the Lipschitz structure in dimensions $\neq 4$. | |
| Jul 20, 2020 at 16:27 | comment | added | Igor Belegradek | @RohilPrasad: I do not know what happens in dimension 4. You now have all the references that I have, and should be able to explore it further. | |
| Jul 20, 2020 at 16:17 | vote | accept | Rohil Prasad | ||
| Jul 20, 2020 at 16:13 | comment | added | Rohil Prasad | This is interesting, thanks. Is there a counterexample in dimension 4? Perhaps one can appeal to Donaldson-Sullivans work on Lipschitz/quasi-conformal 4-manifolds... | |
| Jul 20, 2020 at 0:22 | history | answered | Igor Belegradek | CC BY-SA 4.0 |