Khovanov homology and knot Floer homology for pointed links

John A. Baldwin, Adam Simon Levine, Sucharit Sarkar

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

A well-known conjecture states that for any l-component link L in S3, the rank of the knot Floer homology of L (over any field) is less than or equal to 2l-1 times the rank of the reduced Khovanov homology of L. In this paper, we describe a framework that might be used to prove this conjecture. We construct a modified version of Khovanov homology for links with multiple basepoints and show that it mimics the behavior of knot Floer homology. We also introduce a new spectral sequence converging to knot Floer homology whose E1 page is conjecturally isomorphic to our new version of Khovanov homology; this would prove that the conjecture stated above holds over the field Z2.

Original languageEnglish (US)
Article number1740004
JournalJournal of Knot Theory and its Ramifications
Volume26
Issue number2
DOIs
StatePublished - Feb 1 2017

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Keywords

  • Khovanov homology
  • knot Floer homology

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