Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 21 for “"Symplectic Manifolds"”.
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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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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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A classification of toric, folded-symplectic manifolds
Given a $G$-toric, folded-symplectic manifold with co-orientable folding hypersurface, we show that its orbit space is naturally a manifold with corners $W$ equipped with a smooth map $\psi: W \to \frak{g}^*$, where $\frak{g}^*$ is the dual of the Lie algebra of the torus, $G$. The map $\psi$ has …
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Odd dimensional symplectic manifolds by Zhenqi He.
In this thesis, we introduce the odd dimensional symplectic manifolds. In the first half we study the Hodge theory on the basic symplectic manifolds. We can define two cohomology theories on them, the standard basic de Rham cohomology gheory and a basic version of the Koszul-Brylinski-Mathieu …
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Properties of Hamiltonian Torus Actions on Closed Symplectic Manifolds
… of certain Hamiltonian torus actions on closed symplectic manifolds. First, we will consider counting Hamiltonian torus actions on closed, symplectic manifolds M with 2-dimensional second cohomology. In particular, all such manifolds are bundles with fiber and base equal to projective spaces. We …
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Semi-Free Hamiltonian Circle Actions on Six-Dimensional Symplectic Manifolds
Assume M is a connected, compact 6-dimensional symplectic manifold equipped with a semi-free Hamiltonian circle action such that the fixed point set consists of isolated points or compact orientable surfaces. Assume the second Betti number of M is less than 3. We give a complete list of the …
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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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The Fukaya category, exotic forms and exotic autoequivalences
A symplectic manifold is a smooth manifold M together with a choice of a closed non-degenerate two-form. Recent years have seen the importance of associating an A∞-category to M, called its Fukaya category, in helping to understand symplectic properties of M and its Lagrangian submanifolds. One of …
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Hamiltonian Actions In Integral Kahler And Generalized Complex Geometry
… of the basic case of Hamiltonian actions on symplectic manifolds, and the second a generalization of the basic case. Brion proved a convexity result for the moment map image of an irreducible subvariety of a compact integral Kahler manifold preserved by the complexification a of the …
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Computations in monotone 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 Mirror …
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The symplectic topology of Stein manifolds
Exotic Stein manifolds are 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 …
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Stacks in Poisson geometry
… the question: What is the stack associated to a symplectic groupoid? The last chapter discusses a remarkable class of Poisson manifolds, called b-symplectic manifolds, giving a classification of them up to Morita equivalence and computing their Picard group.
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Mayer-Vietoris property for relative symplectic cohomology
… of a Floer theoretic invariant called relative symplectic cohomology. The construction is based on Hamiltonian Floer theory. It assigns a module over the Novikov ring to compact subsets of closed symplectic manifolds. I show the existence of restriction maps, and prove that they satisfy the …
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Quantum Steenrod operations and Fukaya categories
… introduction of mod p equivariant operations to symplectic Gromov-Witten theory has fueled exciting developments in the field. In this thesis, we develop new tools for understanding these operations and explore an application to the quantum connection. In one direction, we construct certain …
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GKM manifolds with low Betti numbers
A GKM manifold is a symplectic manifold with a torus action such that the fixed points are isolated and the isotropy weights at the fixed points are linearly independent. Each GKM manifold has a GKM graph which contains much of the topological information of the manifold, in particular the …
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Relative Hilbert scheme methods in pseudoholomorphic geometry
… by S. Donaldson and I. Smith aimed at using symplectic Lefschetz fibration techniques to obtain information about pseudoholomorphic curves in symplectic 4-manifolds. Donaldson and Smith introduced an invariant DS which counts holomorphic sections of a relative Hilbert scheme constructed from …
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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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Pseudoholomorphic quilts with figure eight singularity
… together the Fukaya categories of many different symplectic manifolds. I call this object the "symplectic A[infinity]-2-category Symp". The key to defining the structure maps of Symp is the figure eight bubble. In the second part, I establish a collection of strip-width-independent elliptic …
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Equivariant cohomology, homogeneous spaces and graphs
The focus of this thesis is manifolds with group actions, in particular symplectic manifolds with Hamiltonian torus actions. We investigate the relationship between the equivariant cohomology of the manifold M and the fixed point data of the torus action. We are interested in understanding 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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