Timeline for Classification of mapping tori
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Oct 10, 2016 at 5:00 | comment | added | ThiKu | For the second question (in brackets): if the bundles are just diffeomorphic and not bundle-isomorphic, then the mapping classes need not be conjugate. See mathoverflow.net/questions/241822/… | |
| Apr 22, 2010 at 11:31 | comment | added | Jeffrey Giansiracusa | For a diffeotopy it is exactly the same short argument; topologically isotopic maps give homeomorphic bundles, and smoothly isotopic maps give diffeomorphic bundles. And in fact, reducing to the mapping class group is unnecessary. If f and g are isotopic then they are conjugate. | |
| Apr 22, 2010 at 10:32 | comment | added | Sam Nead | I wonder if there is a subtle point lurking here... if $f_0$ and $f_1$ are isotopic (homotopic through homeomorphisms) then the two bundles will be homeomorphic. However, the question asked about diffeomorphism. This is not my area, so I don't see that a diffeotopy (homotopic through diffeomorphisms?) gives a diffeomorphism of bundles... It feels like the "quality" of the derivative of the time direction will be important? | |
| Apr 22, 2010 at 9:00 | history | answered | Jeffrey Giansiracusa | CC BY-SA 2.5 |