Timeline for Approximation of homeomorphism by diffeomorphism
Current License: CC BY-SA 4.0
8 events
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| Dec 19, 2019 at 8:35 | comment | added | Ryan Budney | @MKO: it's not hard to define. Take the oriented homotopy $n$-spheres, up to orientation-preserving diffeomorphism. They have a connect-sum operation, and that operation turns them into a group. Finding non-trivial elements in this group, especially ones that are not 2-torsion is quite a bit more work. Not being 2-torsion means the homotopy-sphere is not diffeomorphic to its orientation-reverse. | |
| Dec 18, 2019 at 18:35 | history | edited | Oscar Randal-Williams | CC BY-SA 4.0 |
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| Dec 18, 2019 at 10:16 | vote | accept | asv | ||
| Dec 18, 2019 at 10:13 | comment | added | asv | This is a great answer. Just one more question: is it hard to define $\Theta_d$? | |
| Dec 18, 2019 at 9:37 | history | edited | Oscar Randal-Williams | CC BY-SA 4.0 |
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| Dec 18, 2019 at 9:11 | comment | added | asv | Thank you very much. Actually you have made two statements: are there references for both of them? | |
| Dec 18, 2019 at 8:40 | comment | added | abx | I suppose this is well-known to experts, but for the others: what would be an example of a homomorphism not isotopic to a diffeomorphism? | |
| Dec 18, 2019 at 8:03 | history | answered | Oscar Randal-Williams | CC BY-SA 4.0 |