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Showing 1 to 14 of 14 for “"Floer theory"”.
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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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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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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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On a Heegaard Floer theory for tangles
… “local” version of Ozsváth and Szabó’s Heegaard Floer homology HFL^ for links in the 3-sphere, i.e. a Heegaard Floer homology HFT^ for tangles in the 3-ball. The decategorification of HFL^ is the classical Alexander polynomial for links; likewise, the decategorification of HFT^ gives a local …
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Surgery Exact Triangles in Instanton Theory
The introduction of instanton Floer theory and Donaldson polynomial invariants in the 1980s revolutionised the study of low dimensional topology. Since then, many Floer theories have been introduced with different structural properties and qualitative features. One of these Floer theories, Heegaard …
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A semi-infinite cycle construction of Floer homology
… with the foundations of a new approach to Floer theory. As opposed to the traditional approach, which can be viewed as a generalization of Morse theory to an infinite dimensional setting, our approach is a generalization of bordism to infinite dimensions. The key new insight, based on …
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Monopoles and Landau-Ginzburg Models
In this thesis, we define the monopole Floer homology for any pair (𝑌, 𝜔), where 𝑌 is any oriented compact 3-manifold with toroidal boundary and 𝜔 is a suitable closed 2-form on 𝑌 , generalizing the construction of Kronheimer-Mrowka for closed 3-manifolds. The basic setup is borrowed from the …
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Mayer-Vietoris property for relative symplectic cohomology
… I construct and investigate the properties 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 …
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Quantum Steenrod operations and Fukaya categories
… 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 operations on the equivariant …
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Slice implies mutant ribbon for odd 5-stranded pretzel knots
… Donaldson's Diagonalization Theorem from gauge theory, and d-invariants from Heegaard-Floer theory. From each of these tools, a necessary condition for sliceness can be extracted and this thesis shows that for odd 5-stranded pretzel knots that are not mutant ribbon, these conditions are not met …
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Aspects of Generalized Geometry: Branes with Boundary, Blow-ups, Brackets and Bundles
… be seen as a first step towards the extension of Floer theory techniques to stable generalized complex geometry, which we hope to develop in future work. The second part of this thesis studies Dorfman brackets, a generalisation of the Courant- Dorfman bracket, within the framework of double vector …
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New techniques in calculation of sutured instanton Floer homology: by Heegaard diagrams, Euler characteristics, and Dehn surgery formulae
… conjectured that sutured instanton Floer homology $SHI(M,\gamma)$ has the same dimension as the sutured Floer homology $SFH(M,\gamma)$ constructed by Juh\'{a}sz for any balanced sutured manifold $(M,\gamma)$. Motivated by their conjecture, we introduce new techniques for calculations …
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The Seiberg-Witten equations on manifolds with boundary
… analysis for constructing a monopole Floer theory on 3-manifolds with boundary.
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Obstructions to the existence of displaceable Lagrangian submanifolds
Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by William Ingram (wingram2@illinois.edu) on 2012-06-27T21:24:50Z Item is restricted until 2014-06-27T21:24:27Z