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Knots in lattice homology

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

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Abstract: Assume that Gamma(v0) is a tree with vertex set Vert(Gamma(v0)) = v(0), v(1),..., v(n), and with an integral framing (weight) attached to each vertex except v(0). Assume furthermore that the intersection matrix of G = Gamma(v0) - v(0) is negative definite. We define a filtration on the chain complex computing the lattice homology of G and show how to use this information in computing lattice homology groups of a negative definite graph we get by attaching some framing to v(0). As a simple application we produce new families of graphs which have arbitrarily many bad vertices for which the lattice homology groups are isomorphic to the corresponding Heegaard Floer homology groups.
Publication Date: 2014
Electronic Publication Date: 25-Nov-2014
Citation: Ozsvath, Peter, Stipsicz, Andras I, Szabo, Zoltan. (2014). Knots in lattice homology. COMMENTARII MATHEMATICI HELVETICI, 89 (783 - 818. doi:10.4171/CMH/334
DOI: doi:10.4171/CMH/334
ISSN: 0010-2571
EISSN: 1420-8946
Pages: 783 - 818
Type of Material: Journal Article
Version: Author's manuscript

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