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.
Results
Showing 1 to 20 of 51 for “"floer"”.
-
Combinatorial Knot Floer Homology
Knot Floer Homology HFK(K) of a knot K in S^3 was defined by Peter Ozsváth and Zoltan Szabó in 2003. It has since become powerful invariant for the study of properties of knots. The definition of the Knot Floer Homology groups initially involved counting holomorphic disks in symmetric products of …
-
Bordered Sutured Floer Homology
… relationship between two versions of Heegaard Floer homology for 3-manifolds with boundary--the sutured Floer homology of Juhasz, and the bordered Heegaard Floer homology of Lipshitz, Ozsvath, and Thurston. We define a new invariant called Bordered sutured Floer homology which encompasses these …
-
Naturality in Heegaard Floer Homology
… between them. We show that the Heegaard Floer invariants yield functors from Man* to the category of transitive systems in the projectivized category of Z[U]-modules, whose values agree with the Heegaard Floer invariants dened by Ozsvath and Szabo. In doing so, we will see that these …
-
Heegaard Floer Invariants and Cabling
… satellite operation of cabling, and on Heegaard Floer-theoretic properties. In particular, we will give a formula for the Ozsvath-Szabo concordance invariant tau of iterated cables of a knot K in terms of the cabling parameters, tau(K), and a new concordance invariant, epsilon(K). We show that, …
-
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.
-
Knot Floer Homology and Categorification
… arising from categorification and from Heegaard Floer homology, we present a self-contained construction of knot Floer homology in the language of HOMFLY-PT homology. Using the cube of resolutions for knot Floer homology defined by Ozsváth and Szabó;, we first give a purely algebraic proof of …
-
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 …
-
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 …
-
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 …
-
Applications of 3-manifold Floer Homology
… preliminaries necessary to understand 3-manifold Floer Homology constructed by Peter Kronheimer and Tomasz Mrowka in [16], along with some properties of this theory, calculations for specific manifolds, and applications to 3-manifold topology.
-
Bordered Heegaard Floer Homology, Satellites, and Decategorification
We use the methods of bordered Floer homology to provide a formula for both τ and HFK of certain satellite knots. In many cases, this formula determines the 4-ball genus of the satellite knot. In parallel, we explore the structural aspects of the bordered theory, developing the notion of an Euler …
-
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 …
-
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 …
-
Twisted Manolescu-Floer spectra for Seiberg-Witten monopoles
… and Kronheimer-Manolescus construction of Floer homotopy type to general 3-manifolds. This Floer homotopy type is a candidate for an object whose suitable homology groups recover Floer homology. The main idea is to apply finite dimensional approximation technique and Conley index theory to …
-
Monopole Floer homology, link surgery, and odd Khovanov homology
… spectral sequence for all versions of monopole Floer homology with mod 2 coefficients, generalizing the exact triangle. The spectral sequence begins with the monopole Floer homology of a hypercube of surgeries on a 3-manifold Y, and converges to the monopole Floer homology of Y itself. This …
-
Quantum and Floer cohomology have the same ring structure
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1996.
-
Bordered Heegaard Floer Homology and four-manifolds with corners
The Heegaard Floer hat invariant is defined on closed 3-manifolds, with a related invariant for 4-dimensional cobordisms, forming a 3+1 topological quantum field theory. Bordered Heegaard Floer homology generalizes this invariant to parametrized Riemann surfaces and to cobordisms between them, …
-
An elementary approach to some aspects of Heegaard Floer homology
Heegaard Floer homology is a new invariant for 3-manifolds and links introduced by Ozsvath and Szabo. It counts pseudo-holomorphic Whitney disks in the symmetric product of the Heegaard surface of the underlying manifold. This thesis is about showing the existence of a natural complex structure on …
-
Contributions to sutured monopole and sutured instanton Floer homology theories
… of sutured monopole and sutured instanton Floer homology theories. Sutured monopole and instanton Floer homologies were introduced by Kronheimer and Mrowka. They are the adaption of monopole and instanton Floer theories to the case of balanced sutured manifolds, which are compact oriented …
-
Results on spectral sequences for monopole and singular instanton Floer homologies
We study two gauge-theoretic Floer homologies associated to links, the singular instanton Floer homology introduced in [15] and the monopole Floer homology, which is explained in the book [16]. For both cases, we study in particular the spectral sequence that relates the Floer homologies to the …
Page 1 of 3