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Showing 1 to 5 of 5 for “"symplectomorphism"”.
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The quantum Johnson homomorphism and symplectomorphism of 3-folds
… class in Hochschild cohomology to every symplectomorphism ... K2,A. These are analogues to the familiar Johnson kernel X9 and second Johnson homomorphism - 2 from low-dimensional topology. The method is quite general, and unlike many abstract tools, explicitly computable in certain nice …
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Distinguishing open symplectic mapping tori via their wrapped Fukaya categories
… of symplectic mapping torus associated to a symplectomorphism from the mapping torus of the identity. As an application, we obtain pairs of diffeomorphic Weinstein domains with the same contact boundary and symplectic cohomology, but that are different as Liouville domains. This work consists …
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The Fukaya category, exotic forms and exotic autoequivalences
… manifold (M,ω), there is an associated symplectomorphism ∅v of M. In Part I, we defi ne the notion of a CPn-object in an A∞-category A, and use this to construct algebraically an A∞- functor Φv , which we prove induces an autoequivalence of the derived category DA. We conjecture that Φv …
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Projective twists and the Hopf correspondence
… fibres, and define a compactly supported symplectomorphism $\varphi \in \mathrm{Symp}_{ct}(T^*\mathbb{A}\mathbb{P}^2)$ on the total space. Given two disjoint Lefschetz thimbles $\Delta_{\alpha},\Delta_{\beta} \subset T^*\mathbb{A}\mathbb{P}^2$, we compute the Floer cohomology groups …
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J - holomorphic curves and their applications
This thesis covers four results: 1. We prove an analog of Whitney's embedding theorem for J-holomorphic discs. 2. For zj = xj + i*yj in C and let D_R^2 = {(z1, z2) in C^2 : x1^2 + x2^2 <1, y1^2 + y2^2 < 1} be the real bi-disc in C^2. We find the sharp lower bound for R such that D_R^2 admits a …