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Showing 1 to 5 of 5 for “"knot Floer homology"”.
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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 …
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Knot Floer Homology and Categorification
… of better 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 …
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Embedded contact knot homology and a surgery formula
Embedded contact homology is an invariant of closed oriented contact 3-manifolds first defined by Hutchings, and is isomorphic to both Heegard Floer homology (by the work of Colin, Ghiggini and Honda) and Seiberg-Witten Floer cohomology (by the work of Taubes). The embedded contact chain complex is …
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Invariance of Knot Lattice Homology and Homotopy
… and complex curves inside them. We prove that knot lattice homology is an invariant of the smooth knot type of a generalized algebraic knot in a rational homology sphere. In that case, knot lattice homology can be realized as the cellular homology of a doubly-filtered homotopy type, which is …