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Showing 1 to 6 of 6 for “"Symplectic topology"”.
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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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Enumerative algebraic geometry via techniques of symplectic topology and analysis of local obstructions
… field that are motivated by recent progress in symplectic topology and its influence on enumerative geometry. The most straightforward applications of the methods developed are to enumeration of rational curves with a cusp of specified nature in projective spaces. A general approach for counting …
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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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Exact Lagrangian Fillings of Legendrian links and Weinstein 4-manifolds
<p> One approach to studying symplectic manifolds with contact boundary is to consider Lagrangian submanifolds with Legendrian boundary; in particular one can study exact Lagrangian fillings of Legendrian links. There are still many open questions on the spaces of exact Lagrangian fillings of …
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Projective twists and the Hopf correspondence
… is the fruit of a research project on a class of symplectic automorphisms called $projective$ $twists$. In the first part of the thesis (Chapters 3,4) we use Picard$-$Lefschetz theory to introduce a new local model for the planar projective twists $\tau_{\mathbb{A}\mathbb{P}^2} \in …
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Symmetry in monotone Lagrangian Floer theory
… 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 the Oh spectral sequence to coefficients of …