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I realise I don't have a good definition for the vertical tangent bundle in the case of a Lefschetz fibration $(E,F)\to (S,\partial S)$ ($F$ is the subbundle given by the tangent bundle of the Lagrang …

I’m asking this question because I’d like to understand better the neck-stretching argument in symplectic geometry and what kind of conclusions one might get out of it in my setting. Assume that I’ve …

I'm trying to understand why in the following lemma (Lemma 10.7 of [BEHWZ]), the upper bound on the $L^{\infty}$-norm of the differential is given in terms of the injective radius w.r.t to a specific …

I'm trying to get some intuition for the Conley-Zehnder index in the setting of Floer homology of a symplectomorphism $\phi : (M,\omega) \to (M,\omega)$. Let's assume that $\phi$ only has non-degenera …

I'm looking for a clarification of a construction done in Seidel's Symplectic Floer Homology of a Dehn twist: I don't get why his choice of almost complex structure on $\Sigma$ is a valid one for writ …

I'm trying to find out the motivations that led V. Arnold to formulate his famous conjecture (I guess theorem by now) in the following form: Let $(M,\omega)$ be a closed symplectic manifold (add what …

As the title suggests, I want to understand the strip breaking phenomenon that happens when I Gromov-compactify the moduli space of pseudoholomorphic curves from the holomorphic strip $\Bbb R \times [ …

Let us consider the space of configurations $\overline{\mathcal{M}}_{0,2,1,(1,1)}$ of an annulus with a marked point on the interior boundary component (let's call it "out") a marked point on the exte …

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 bou …

I'm interested in understanding better the properties of the integrable (almost) complex structure that Eliashberg constructs on the cotangent bundle of a closed manifold $M$, whose dimension is at le …

Is there any reference in the literature about results regarding symplectic field theory (SFT) compactness for a neck-stretch in the context of Floer homology of a symplectomorphism $\phi \colon (M,\o …

This question is related to my old question Bubbling off of a pseudo holomorphic sphere on surface with cylindrical ends about the bubbling off argument in Seidel's paper The symplectic Floer homology …

I'm computing the product map $$\mu_2 : CF(L_0,V)\otimes CF(V,L_1)\to CF(L_0,L_1)$$ in Seidel's exact triangle for this specific case: This is a genus 2 surface, and I color-coded the three (Lagrangi …

I'm looking for some help in understanding the PSS isomorphism map in the context of Hamiltonian Floer cohomology and Morse cohomology with universal Novikov coefficients $\Lambda_{\omega}$ (à la Seid …

Let's take a Riemann surface $\Sigma$ and three Lagrangians $L_0,L_1,L_2$ in general position. let's assume that we can set up Lagrangian Floer (co)homology - Here I'm being vague because I don't want …