Knots in lattice homology

Peter Ozsváth, András I. Stipsicz, Zoltán Szabó

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

Assume that Fv0 is a tree with vertex set Vert (Fυ0) = {v0, v1, ... , vn}, and with an integral framing (weight) attached to each vertex except v0. Assume furthermore that the intersection matrix of G = Fv0 - {v0} 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 υ0. 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.

Original languageEnglish (US)
Pages (from-to)783-818
Number of pages36
JournalCommentarii Mathematici Helvetici
Volume89
Issue number4
DOIs
StatePublished - 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Heegaard Floer homology
  • Knot Floer homology
  • Lattice homology

Fingerprint Dive into the research topics of 'Knots in lattice homology'. Together they form a unique fingerprint.

  • Cite this