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8
votes
0answers
434 views

SFT gluing on chain level in Floer homology?

I came across a new type of gluing in the FOOO paper http://arxiv.org/abs/1002.1660 (maybe not so new to experts). The situation is as follows: one considers a relative (to lagrangian) class and ...
7
votes
0answers
373 views

Degenerate moduli spaces in Floer homology

Let $(W,\omega)$ be a closed symplectially aspherical symplectic manifold, and fix a Hamiltonian $H\in C^{\infty}(W\times S^{1};\mathbb{R})$ and a compatible almost complex structure $J$ on $W$. Given ...
5
votes
0answers
129 views

Unobstructed Lagrangian tori

Let $X$ be a compact symplectic manifold, $U$ a Darboux chart, and $L$ a standard Lagrangian torus in $U$. Is $H^1(L)$ weakly unobstructed in the sense of Fukaya-Oh-Ohta-Ono (that is, does $b \in ...
4
votes
0answers
122 views

What can be said about compact embedded exact Lagrangians in the generalized pair of pants?

What can be said about compact embedded exact Lagrangians in the $n$-dimensional generalized pair of pants e.g. the hypersurface in $(\mathbb{C}^*)^{n+1}$ defined by the equation: $$ 1+\Sigma_i z_i = ...
4
votes
0answers
228 views

Lie-infinity structure in Lagrangian Floer theory ?

Is there (besides the A-infinity structure) also a L-infinity structure in Lagrangian Floer theory (forming together a G-infinity structure) - like in Hochschild cohomology ?
3
votes
0answers
192 views

Regular points for solutions of Floer's equation

Let $(W,\omega)$ be a symplectic manifold and $H\in C^{\infty}(W\times S^{1};\mathbb{R})$. Let $(J_{t})_{t\in S^{1}}$ denote a family of $\omega$-compatible almost complex structures. Fix a map $u\in ...
2
votes
0answers
173 views

$C^0$ estimates in wrapped Lagrangian Floer cohomology

Let $(M, d\theta, \theta, Z)$, be an exact Liouville domain, where $Z$ is the Liouville vector field and $\theta$ is the primitive of the symplectic form. Let $\bar{M}$, be the symplectic completion ...
2
votes
0answers
134 views

Spin-c structures for a closed,oriented 3-manifold equipped with a null homologous knot

Let $Y$ be a closed, oriented 3-manifold equipped with an oriented null homologous knot $K$. I want to understand the relative $spin^c$ structures for $(Y,K)$. There is canonical zero surgery ...
0
votes
0answers
114 views

Gromov-Floer compactness for C^0 convergence of complex structure/ C^1 convergence of Hamiltonian

Let $M$ be a compact symplectic manifold, $J$ a possibly surface dependent complex structure, and $H$ a Hamiltonian on $M$. I am interested in a variant of Gromov-Floer convergence for solutions of ...
0
votes
0answers
159 views

why $H_{1}(\Sigma)\cong H_{1}(Sym^{g}(\Sigma))$ ?

In paper holomorphic disks and 3-manifold invariants, Ozsvath and Szabo connstruct two homeomoephisms $\mathcal {f} : H_{1}(\Sigma)\rightarrow H_{1}(Sym^{g}(\Sigma))$ and $\mathcal {g} : ...