Knots in lattice homology

  • Peter S. Ozsváth

    Princeton University, USA
  • András I. Stipsicz

    Hungarian Academy of Sciences, Budapest, Hungary
  • Zoltán Szabó

    Princeton University, USA


Assume that is a tree with vertex set , and with an integral framing (weight) attached to each vertex except . Assume furthermore that the intersection matrix of is negative definite. We define a filtration on the chain complex computing the lattice homology of and show how to use this information in computing lattice homology groups of a negative definite graph we get by attaching some framing to . 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.

Cite this article

Peter S. Ozsváth, András I. Stipsicz, Zoltán Szabó, Knots in lattice homology. Comment. Math. Helv. 89 (2014), no. 4, pp. 783–818

DOI 10.4171/CMH/334