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 32 for “"Floer homology"”.
-
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 …
-
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
… understanding the connections between knot homology theories 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 …
-
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 …
-
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 …
-
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 …
-
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 …
-
The Surgery Exact Triangle in Monopole Floer Homology with Z[i] Coefficients
… of a surgery exact triangle for Monopole Floer homology. The triangle was a theoretical breakthrough and allowed us to answer questions about the surgery correspondence between knots and 3-manifolds that were previously mysterious. A serious limitation of their triangle was that it only …
-
Group actions, cobordisms, and other aspects of 4-manifold theory through the eyes of Floer homology
Thesis (Ph. D.)--Michigan State University. Mathematics, 2010
-
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 …
-
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 …
-
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 …
-
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 …
-
Broken Lefschetz fibrations, Lagrangian matching invariants and Ozsváth-Szabó invariants
… 3-manifold invariants, namely Perutz's quilted Floer homology and Ozsváth-Szabó Heegaard Floer homology for certain spinc structures. This yields interesting and in a sense simplified geometric interpretations of Ozsváth-Szabó invariants. In particular, we give new calculations of these …
-
Monopoles and Pin(2)-symmetry
… we generalize the construction of monopole Floer homology due to Kronheimer and Mrowka to the case of a gradient flow with Morse-Bott singularities. Focusing then on the special case of a three-manifold equipped equipped with a spinc structure which is isomorphic to its conjugate, we define …
-
Spectral Fukaya Categories for Liouville Manifolds
… stable homotopy types underlying symplectic Floer homology, realizing a program proposed by Cohen, Jones and Segal twenty-five years ago. We work in the setting of Liouville manifolds with a stable symplectic trivialization of their tangent bundles, where we prove that the moduli spaces of …
Page 1 of 2