Timeline for Question about the dimension of a Contact (Symplectic) manifold
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 21, 2011 at 23:57 | vote | accept | Phi Le | ||
| Feb 21, 2011 at 9:52 | answer | added | José Figueroa-O'Farrill | timeline score: 7 | |
| Feb 21, 2011 at 3:06 | comment | added | Deane Yang | I agree that José should post his comment as an answer. | |
| Feb 21, 2011 at 2:44 | comment | added | Theo Johnson-Freyd | @Jose: This should probably be an answer, not a comment. Since that the answer is a comment, I'm tempted to vote to close as "no longer relevant". | |
| Feb 21, 2011 at 2:16 | comment | added | José Figueroa-O'Farrill | Your guess is correct. Contact structures are structures associated to a one-form $\alpha$ with maximal rank. There are two cases: for odd rank, you want $\alpha \wedge (d\alpha)^k$ to be nowhere vanishing for the largest possible $k$ allowed by dimension, or even rank, with the same condition on $(d\alpha)^k$. In the former case you have a contact structure and in the latter an exact symplectic structure. Symplectic forms are nondegenerate by definition, so this can only happen if the dimension is even. (I'm assuming finite-dimensionality throughout.) | |
| Feb 21, 2011 at 1:54 | history | edited | David Roberts♦ |
Added tag
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| Feb 21, 2011 at 1:52 | history | asked | Phi Le | CC BY-SA 2.5 |