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Showing 1 to 20 of 172 for “"Symplectic"”.
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Rigidity of symplectic fillings, symplectic divisors and Dehn twist exact sequences
We present three different aspects of symplectic geometry in connection to complex geometry. Convex symplectic manifolds, symplectic divisors and Lagrangians are central objects to study on the symplectic side. The focus of the thesis is to establish relations of these symplectic objects to the …
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Irreducible symplectic complex spaces
… deduce a local Torelli theorem for irreducible symplectic complex spaces. As an application of the local Torelli theorem, we prove that irreducible symplectic complex spaces whose codimension of the singular locus does not deceed $4$ satisfy the so-called Fujiki relation.
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Symplectic and complex foliations
"Symplectic (not necessarily Riemannian) foliations have a transversely symplectic structure for which many standard results of symplectic geometry have their transverse analogues: the dual bundle to the transverse bundle of a foliation is a manifold with a canonical symplectic foliation, the …
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Questions around symplectic capacities
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-19 without embargo terms
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Geometry and representation theory of symplectic singularities in the context of symplectic duality
… geometry and representation theory of various symplectic resolutions of singularities from different perspectives. Specifically, following the ideas of Bellamy, Hilburn, Kamnitzer, Tingley, Webster, Weekes, and Yacobi, we establish a general approach to attack the Hikita-Nakajima conjecture and …
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Folded Symplectic Toric Four -Manifolds
A folded symplectic form on an even-dimensional manifold is a closed two-form that degenerates in a suitably controlled way along a smooth hypersurface. When a torus having half the dimension of the manifold acts in a way preserving the folded symplectic form and admitting a moment map, the …
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Deformation quantization of symplectic fibrations
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1996.
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Symplectic isotopy for cuspidal curves
… that if the first Chern class of a 4-dimensional symplectic manifold is sufficiently positive then the deformation is unobstructed. We prove this result when the curves have cusps and nodes, not in a prescribed position. We also prove a similar result when the curves have cusps and tacnodes in a …
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Topological invariants of symplectic quotients
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1997.
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Symplectic properties of Milnor fibres
We present two results relating to the symplectic geometry of the Milnor fibres of isolated affine hypersurface singularities. First, given two Lagrangian spheres in an exact symplectic manifold, we find conditions under which the Dehn twists about them generate a free non-abelian subgroup of the …
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Symplectic cohomology of contractible surfaces
… products of this manifold provide non-standard symplectic structures on Euclidean space which are convex at infinity. I extend these techniques a wide class of smooth contractible affine surfaces of log-general type to produce a similar torus. I then show that the existence of this torus implies …
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The symplectic topology of Stein manifolds
… diffeomorphic to JR2 k which cannot be embedded symplectically into the Stein manifold <r:,k. In this thesis we prove two results about exotic Stein manifolds. The first result shows us that in each complex dimension > 2, there exists an exotic Stein manifold which is not symplectomorphic to any …
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Topics in symplectic Gromov–Witten theory
… is on the Gromov--Witten theory of general symplectic manifolds. Mohan Swaminathan and I construct a framework to define a virtual fundamental class for the moduli space of stable maps to a general closed symplectic manifold. Our construction, inspired by [AMS21], works for all genera and …
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Symplectic Frölicher spaces of constant dimension
Includes bibliographical references (leaves 113-121).
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Exotic symplectic manifolds from Lefschetz fibrations
… but are not symplectomorphic. While W0 is symplectically very similar to the cotangent bundle itself, W1 is 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 …
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Scalar Curvature Constraints on Symplectic 4-Manifolds
… interplaybetween Riemannian geometry and symplectic topology on 4-manifolds. These two branches of mathematics belong to different worlds: Where geometry concerns it- self with distances, angles, areas, curvatures, etc., all of which typically vary from one point on the manifold to the …
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Multi-Symplectic Integrators for Nonlinear Wave Equations
<p>Symplectic (area-preserving) integrators for Hamiltonian ordinary differential equations have shown to be robust, efficient and accurate in long-term calculations. In this thesis, we show how symplectic integrators have a natural generalization to Hamiltonian PDEs by introducing the concept of …
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Homogeneous Symplectic Manifolds of the Galilei Group
<p>In this thesis we classify all symplectic manifolds admitting a transitive, 2-form preserving action of the Galilei group G. Using the moment map and a theorem of Kirillov-Kostant-Souriau, we reduce the problem to that of classifying the coadjoint orbits of a central extension of G discovered by …
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