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Showing 1 to 10 of 10 for “"Floer cohomology"”.
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Quantum and Floer cohomology have the same ring structure
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1996.
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Floer cohomology in the mirror of the projective plane and a binodal cubic curve
… of the twisting sheaf 0(1), and hence their Floer cohomology groups form an algebra isomorphic to the homogeneous coordinate ring. An interesting feature is the presence of a singular torus fibration on the mirror, of which the Lagrangians are sections. This gives rise to a distinguished …
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Localization and Heegaard Floer Homology
… we use Seidel-Smith localization for Lagrangian Floer cohomology to study invariants of cyclic branched covers of three-manifolds and symmetry groups of knots by constructing localization spectral sequences in Heegaard Floer homology.
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Floer theory and spectral networks
… non-abelianization map and Floer theory. Given a complete GMN quadratic differential $\phi$ defined on a closed Riemann surface $C$, let $\tilde{C}$ be the complement of the poles of $\phi$. In the case where the spectral curve $\Sigma_{\phi}$ is exact with respect to the …
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Exotic symplectic manifolds from Lefschetz fibrations
… more unusual. I use Seidel's exact triangles for Floer cohomology to show that the wrapped Fukaya category of W1 is trivial. As a corollary we obtain that W1 contains no compact exact Lagrangian submanifolds.
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Spectral Fukaya Categories for Liouville Manifolds
… stable homotopy types underlying symplectic Floer homology, realizing a program proposed by Cohen, Jones and Segal twenty-five years ago. We work in the setting of Liouville manifolds with a stable symplectic trivialization of their tangent bundles, where we prove that the moduli spaces of …
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Symmetry in monotone Lagrangian Floer theory
In this thesis we study the self-Floer theory of a monotone Lagrangian submanifold $L$ of a closed symplectic manifold $X$ in the presence of various kinds of symmetry. First we consider the group $\mathrm{Symp}(X, L)$ of symplectomorphisms of $X$ preserving $L$ setwise, and extend its action on …
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Computations in monotone Floer theory
Floer theory is a rich collection of tools for studying symplectic manifolds and their Lagrangian submanifolds with the help of holomorphic curves. Its origins lie in estimating the numbers of equilibria in Hamiltonian dynamics, and more recently it has become a major component of the Homological …
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Embedded contact knot homology and a surgery formula
… by Hutchings, and is isomorphic to both Heegard Floer homology (by the work of Colin, Ghiggini and Honda) and Seiberg-Witten Floer cohomology (by the work of Taubes). The embedded contact chain complex is defined by counting closed orbits of the Reeb vector field and certain pseudoholomorphic …
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Projective twists and the Hopf correspondence
… T^*\mathbb{A}\mathbb{P}^2$, we compute the Floer cohomology groups $\operatorname{HF}(\varphi^k(\Delta_{\alpha}), \Delta_{\beta};\mathbb{Z}/2\mathbb{Z})$ and verify (partially for $\mathbb{C}\mathbb{P}^2$) that $\varphi$ is indeed isotopic to (a power of) the standard local projective twist. …