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 Yearling
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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
comment Symplectic manifold question.
What part of this is unclear? Is it the notation? or is it the definition of this map $\Phi_p$?
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
Mar
15
comment Is $f(x)+\sum_{p,i=1,…,m}\lambda_{p,i}x_{p,i}(x)$ globally defined?
Where is this question coming from? This seems pretty unmotivated.
Mar
15
answered What does it mean by saying that $u^n, J^n$ “$C^{\infty}$ converges” to u, J?