Timeline for Action of diffeomorphism group on non-vanishing vector fields
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 12, 2019 at 11:14 | vote | accept | ThorbenK | ||
| Dec 7, 2018 at 15:12 | comment | added | Ian Agol | Yes, the connection with maps to $S^2$ depends on a framing. One can ensure that the automorphisms preserve framing (trivialization) by pulling back a framing from downstairs. | |
| Dec 7, 2018 at 7:21 | comment | added | ThorbenK | That confused me earlier. Cobordism classes of framed links correspond to $[M, S^2]$, which is of course also the space of homotopy classes of non-vanishing vector fields. But there are different actions at play here right? The action on framed links is just given by precompoaition, while the push forward action on vector fields also twists the S^2 fibers of the tangent bundle so it does not just act via precompoaition. | |
| Dec 7, 2018 at 3:55 | comment | added | Ian Agol | @ThorbenK: from the viewpoint of the equivalence with framed cobordism classes of framed knots/links, one can see that orientation preserving actions preserve the framing, so act trivially. | |
| Dec 6, 2018 at 19:05 | comment | added | ThorbenK | Furthermore is it known wether this action is transitive or at least far from trivial? | |
| Dec 6, 2018 at 8:27 | comment | added | ThorbenK | Is the action on $\pi_0(\Gamma(TM\setminus 0))$ for isometries of a manifold whose first de rham cohomology vanishes trivial, because in this case we can nicely identify vector fields with 1-forms? | |
| Dec 6, 2018 at 6:32 | history | edited | Ian Agol | CC BY-SA 4.0 |
added 135 characters in body
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| Dec 6, 2018 at 2:55 | history | answered | Ian Agol | CC BY-SA 4.0 |