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Knot lattice homology in L-spaces

Author(s): Ozsvath, Peter Steven; Stipsicz, Andras I; Szabo, Zoltan

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Abstract: We show that the knot lattice homology of a knot in an L-space is chain homotopy equivalent to the knot Floer homology of the same knot (viewed these invariants as filtered chain complexes over the polynomial ring Z/2Z[U]). Suppose that G is a negative definite plumbing tree which contains a vertex w such that G - w is a union of rational graphs. Using the identification of knot homologies we show that for such graphs the lattice homology HF-(G) is isomorphic to the Heegaard Floer homology HF-(Y-G) of the corresponding rational homology sphere Y-G.
Publication Date: Jan-2016
Electronic Publication Date: 15-Dec-2015
Citation: Ozsvath, Peter, Stipsicz, Andras I, Szabo, Zoltan. (2016). Knot lattice homology in L-spaces. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 25 (10.1142/S0218216516500036
DOI: doi:10.1142/S0218216516500036
ISSN: 0218-2165
EISSN: 1793-6527
Type of Material: Journal Article
Journal/Proceeding Title: JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS
Version: Author's manuscript



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