Timeline for Gompf's invariant of $2$-plane fields
Current License: CC BY-SA 3.0
8 events
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| Nov 24, 2014 at 23:27 | comment | added | nikita | There is a discussion in the same book about two contact structures are homotopic iff their so-called $d_2$ and $d_3$ (the last one is the same as $\theta$ in your notation) invariants are equal. | |
| Nov 24, 2014 at 23:13 | comment | added | nikita | Look at page 194 of this book: "Surgery on contact 3-manifolds and Stein structures" by Ozbagci and Stipsicz. They explain how to build a 4-manifold $(X,J)$ with $\partial X=M$. This is the rough idea: start with a contact surgery link of $M$. Look at the corresponding 4-manifold $X$ obtained by attaching 2-handles to this link. $X$ should admit an achiral Lefschetz fibration. Away from the singular points, let $J$ be $\pi/2$-rotation on the tangent plane of fibers. Now we can extend $J$ to neighborhoods of the singular points, since there are honest complex charts near them. | |
| Nov 15, 2014 at 6:49 | comment | added | Math1016 | I have tried to read Kronheimer and Mrowka's book "Monopoles and 3-Manifolds." An answer of my questions is Proposition 28.1.2 in this book, isn't it? Although I have understood substantially a construction of an almost complex manifold we want, I've not understood how to extand this structure to the 4-manifold with boundary $S^1 \times S^2$. Could you explain that to me? | |
| Nov 15, 2014 at 0:16 | comment | added | Tim Perutz | There's also a nice discussion in Kronheimer-Mrowka's paper "Monopoles and contact structures." | |
| Nov 14, 2014 at 21:48 | comment | added | Liviu Nicolaescu | Have you looked at Kronheimer and Mrowka's book Monopoles and 3-Manifolds? | |
| Nov 14, 2014 at 19:47 | history | edited | j.c. | CC BY-SA 3.0 |
typos and contact geometry tag
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| Nov 14, 2014 at 17:41 | review | First posts | |||
| Nov 14, 2014 at 18:04 | |||||
| Nov 14, 2014 at 17:37 | history | asked | Math1016 | CC BY-SA 3.0 |