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        Questions tagged [symplectic-topology]

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        2
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        1answer
        76 views

        Every symplectic submanifold is J-holomorphic

        I am trying to show that every symplectic submanifold $N$ of a 2n- dimensional symplectic manifold $(M,\omega)$ is J-holomorphic for some compatible almost complex structure $J$. The way I am ...
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        vote
        0answers
        34 views

        Invariance under tame almost complex structure of the fibre tangent space of the symplectic normal bundle

        I am trying to understand the construction of symplectic inflation and I am stuck in the following point. Suppose we have a 4 dimensional symplectic manifold $(M, \omega)$. Also suppose that $N \...
        3
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        0answers
        106 views

        Legendrian surgery and invertible elements in zeroth degree symplectic cohomology

        Is there anything known about the relation between Legendrian handle attachment and invertible elements in $\mathit{SH}^0(M)$? As the simplest interesting case, take $M_0$ to be the cotangent bundle $...
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        0answers
        42 views

        What is the relation between the different generating functions thought as finite approximations of action functionals

        In the book Introduction to symplectic topology by MC Duff and Salamon, a discrete analogue of the action functional is defined on $\mathbb{R}^{2n}$. The idea is that a Hamiltonian isotopy can be ...
        3
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        0answers
        94 views

        Mixed characteristic in symplectic geometry

        Are there any mixed-characteristic phenomena in symplectic geometry/mirror symmetry? There are papers on symplectic geometry by Abouzaid (inspired by Kontsevich--Soibelman, I believe) in which there ...
        5
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        1answer
        222 views

        Relationship between Gromov-Witten and Taubes' Gromov invariant

        Fix a compact, symplectic four-manifold ($X$, $\omega$). Recall Taubes' Gromov invariant is a certain integer-valued function on $H^2(X; \mathbb{Z})$ defined by weighted counts of pseudoholomorphic ...
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        2answers
        713 views

        Does Fukaya see all symplectic topology?

        I recently had a debate with my friend about how much of symplectic topology is about Fukaya category. I thought that for the most part, symplectic topology is not about Fukaya category. Now, to prove ...
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        0answers
        85 views

        Maslov index of pair of paths in $\mathcal{L}(2n)$ and its relation with the Maslov index of a loop in $\mathcal{L}(2n)$

        I'm reading [RS] and I was wondering what kind of connection there is between the Maslov index for a pair of paths $\lambda_0,\lambda_1 \colon [a,b] \to \mathcal{L}(2n)$ as defined in [RS] and the ...
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        0answers
        81 views

        A clarification in the definition of Seidel's absolute Maslov index for a pair of transverse Lagrangians

        I'm reading Seidel's paper Graded Lagrangian submanifolds where he introduces the absolute Maslov index of a pair of graded lagrangians as follows: Let $\mathcal{L}(V,\beta)$ be the Lagrangian ...
        3
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        2answers
        157 views

        Symplectic vector fields everywhere transverse to a co-dimension one hypersurface

        Usually when speaking about vector fields transverse to a hypersurface in a symplectic manifold, we talk about Liouville vector fields, i.e. vector fields $X$ with the property that $\mathcal{L}_X\...
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        vote
        1answer
        181 views

        Floer equation and Cauchy Riemann equation

        Consider a symplectic manifold $(M,\omega)$ with the property that $\pi_2(M) = 0$. Given a time dependent hamiltonian $H_t$ on $M$, and a $\omega$-compatible almost complex structure J on M, we may ...
        2
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        0answers
        91 views

        Limitations of the splitting construction and SFT

        I am trying to understand the so-called symplectic field theory (SFT) machinery used in symplectic topology. As I understand it, one of the applications of SFT (or rather, of the splitting ...
        2
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        0answers
        67 views

        Transitivity of Diff on the space of embeddings of balls

        Given 2 symplectic embeddings $g_0$ and $g_1$ of a 4-ball of radius $r \leq 1$ into the 4-ball of radius 1 (all equipped with the standard symplectic form coming from $\mathbb{R}^4$), does there exist ...
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        0answers
        72 views

        Pairs of J-holomorphic curves

        Let $(M, \omega)$ be a symplectic 4-manifold and let $A$ and $B$ be symplectic submanifolds on M such that $A \cap B = p \in M$.Under what conditions can I find a $\omega$-compatible almost complex ...
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        1answer
        212 views

        Intuition about bubbling off a ghost bubble

        I'm trying to improve my intuition about the bubbling phenomenon for $J$-holomorphic curves $\Sigma \to (M,\omega)$, where $\Sigma$ is a compact Riemann surface with possibly boundary. I assume that ...

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