Sam Lisi
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 Mar 16 awarded Yearling Nov 22 awarded Custodian Oct 2 awarded Nice Answer Mar 16 awarded Yearling Mar 10 comment symplectic surfaces in 4-manifolds Off the top of my head, I would guess that if the $\omega$ area of the homology class is positive, you can probably find a symplectic representative, but I haven't thought enough about this. Let me know if this modification of your question is of interest. Mar 10 answered symplectic surfaces in 4-manifolds Feb 18 awarded Custodian Feb 18 comment Non-commutative symplectic geometry Do you have a reference for non-commutative symplectic geometry? I've never heard of this, and am curious. Dec 1 comment Is this some kind of trick question? Submanifold “proof” What is your definition of submanifold? This is indeed a simple exercise once you have stated the correct calculus theorem. Sep 24 awarded Autobiographer May 17 answered When is symplectic pullback bundle trivial May 16 awarded Revival Apr 18 awarded Enlightened Apr 18 awarded Nice Answer Apr 6 comment Symplectic submanifolds in $\mathbb{R}^{4}$ @studiosus: your example isn't relevant to my claim because the punctured surface isn't a manifold with boundary. However, I think you are right that the actions on the boundary are relevant. I'll adjust my answer accordingly. Thank you. Apr 5 comment Symplectic submanifolds in $\mathbb{R}^{4}$ @studiosus: Thank you for the corrected reference. In this case, since the surfaces are compact with boundary, I think it's possible to make some minor modifications to Moser so that it works. In particular, I believe you can modify Moser's proof by hand to make the flow of the vector field he constructs be defined up to time 1. Since that's the piece where compactness is necessary, I think everything else should carry through. Apr 3 comment Symplectic submanifolds in $\mathbb{R}^{4}$ you didn't mention that you had cross-posted this to MO! Next time, be sure to mention it when you do, so we don't waste time duplicating effort. Apr 3 answered Symplectic submanifolds in $\mathbb{R}^{4}$ Mar 16 awarded Yearling Mar 15 answered vector bundles and their cross-sections