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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.|
|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|
|Pages:||783 - 818|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||COMMENTARII MATHEMATICI HELVETICI|
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