# 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 Journal/Proceeding Title: COMMENTARII MATHEMATICI HELVETICI Version: Author's manuscript