Timeline for Contact structure on a circle bundle over a symplectic manifold.
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 30, 2010 at 19:19 | comment | added | Mohammad Farajzadeh-Tehrani | My question is local, so I am interested just in a small neighborhood of D in L. | |
| Apr 30, 2010 at 12:06 | comment | added | Tim Perutz | This, presumably, is symplectic near the zero-section only, in general? Anyway, I concur that if $e$ isn't a multiple of $[w]$, this form is not exact on circle-bundles in $L$, and that conversely, a multiple of a connection form with curvature $const. w$ is contact. | |
| Apr 30, 2010 at 5:41 | comment | added | Mohammad Farajzadeh-Tehrani | Lets fix a hermitian metric on L and let r be the distance function. for $\pi:L\rightarrow D$ consider the two form : $\tilde{w} = π^*w+ r \pi^*e + dr ∧ \beta$ Where $\beta$ is the connection one-form on L\{zerosection} satisfying $\beta{\partial{\theta}}=1$. $\tilde{w}$ extends across D and its restriction to D is $w$. See page 15 of annals paper:" The symplectic sum formula for Gromov-Witten invariants" | |
| Apr 30, 2010 at 1:36 | comment | added | Tim Perutz | How do you construct the symplectic form on $L$? | |
| Apr 29, 2010 at 21:08 | answer | added | Mohammad Farajzadeh-Tehrani | timeline score: 2 | |
| Apr 29, 2010 at 20:56 | answer | added | Liviu Ornea | timeline score: 2 | |
| Apr 29, 2010 at 16:52 | history | edited | Mohammad Farajzadeh-Tehrani | CC BY-SA 2.5 |
added 12 characters in body
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| Apr 29, 2010 at 16:08 | history | asked | Mohammad Farajzadeh-Tehrani | CC BY-SA 2.5 |