Knot lattice homology in L-spaces

Peter Ozsváth, András I. Stipsicz, Zoltán Szabó

Research output: Contribution to journalArticle

Abstract

We show that the knot lattice homology of a knot in an L-space is chain homotopy equivalent to the knot Floer homology of the same knot (viewed these invariants as filtered chain complexes over the polynomial ring Z/2Z[U]). Suppose that G is a negative definite plumbing tree which contains a vertex w such that G-w is a union of rational graphs. Using the identification of knot homologies we show that for such graphs the lattice homology HF-(G) is isomorphic to the Heegaard Floer homology HF-(YG) of the corresponding rational homology sphere YG.

Original languageEnglish (US)
Article number1650003
JournalJournal of Knot Theory and its Ramifications
Volume25
Issue number1
DOIs
StatePublished - Jan 1 2016

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Keywords

  • Knot
  • L-space
  • knot Floer homology
  • lattice homology

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