0
votes
0answers
83 views

filling by holomorphic disks method

Can you give me a reference for the proof of the filling by holomorphic disks method, besides Bishop's original paper?
4
votes
2answers
221 views

Does the 4-sphere have a nonzero Poisson structure as a Poisson homogeneous space?

It is known that the 4-sphere does not have a symplectic structure. However, it does admit Poisson structures, for example the zero Poisson structure, which is quite boring. Does it have other, more ...
11
votes
4answers
1k views

How Many 4-Manifolds are Symplectic?

As an honest question (probably with some subjectivity), how many smooth oriented 4-manifolds are actually symplectic? Can I say half (perhaps under some mild assumptions)? I ask this question because ...
2
votes
1answer
476 views

Problem:Gromov-Witten;Moduli space

Let us consider a map from a $\Sigma_g \longrightarrow N$, where $N$ is a symplectic manifold. Then we define the moduli space as $M= \{ f | f \mbox{ is a pseudoholomorphic map } \Sigma_g \to N, ...
11
votes
1answer
584 views

Where are $+$, $-$ and $\infty$ in bordered Heegaard-Floer theory?

Here goes my first MO-question. I've just read Lipshitz, Ozsváth and Thurston's recently updated "A tour of bordered Floer theory". To set the stage let me give two quotes from this paper. ...
7
votes
1answer
554 views

Are there symplectic 4-folds with $b_+>1$, $b_-=0$?

This is the question. Is it known that a symplectic $4$-fold with $b_2>1$ should have a homology class $C$ with $C^2<0$?
7
votes
1answer
589 views

Gromov-Witten invariants counting curves passing through two points

Let us say that a closed symplectic manifold $X$ is $GW_g$-connected if there is a nonvanishing Gromov-Witten invariant of the form $GW_{g,n}^{X,A}(\beta,point, point,\alpha_3,\ldots,\alpha_n)$ --in ...