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Showing 1 to 15 of 15 for “"Heegaard Floer Homology"”.
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Naturality in Heegaard Floer Homology
… dieomorphisms 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 …
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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.
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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 …
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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, …
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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 …
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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 …
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On planar rational cuspidal curves
… curves from a result of Borodzik-Livingston in Heegaard-Floer homology. Using these constraints and other tools from algebraic geometry, we offer a solution to certain cases of the Coolidge-Nagata problem on the rectifiability of planar rational cuspidal curves, that is, their equivalence to …
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Bordered Sutured Floer Homology
… the 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 …
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Ozsva?th-Szabo? invariants of contact surgeries
… to look at contact manifolds through the eyes of Heegaard Floer homology, by computing their Ozsvath-Szab6 invariants. It's a classical result that doing negative contact surgeries along Legendrian links in ( S3, tst) yields back tight (in fact, Stein fillable) contact structures, so I am going to …
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On a Heegaard Floer theory for tangles
… define a “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 …
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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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Obstructions to slicing knots and splitting links
… space-time. In the first half, we use Khovanov homology to the study the relationship between links in R3 and their components. We construct a new spectral sequence beginning at the Khovanov homology of a link and converging to the Khovanov homology of the split union of its components. The page …
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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 …
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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 untwisting number of a knot
… a different approach to get conditions on the Heegaard Floer correction terms of the branched double cover of a knot with untwisting number one. This allows us to show that several 10-and 11-crossing knots cannot be unknotted by a single positive or negative generalized crossing change. We also …