Khovanov homology and knot Floer homology for pointed links

Published

Journal Article

A well-known conjecture states that for any [Formula: see text]-component link [Formula: see text] in [Formula: see text], the rank of the knot Floer homology of [Formula: see text] (over any field) is less than or equal to [Formula: see text] times the rank of the reduced Khovanov homology of [Formula: see text]. 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 [Formula: see text] page is conjecturally isomorphic to our new version of Khovanov homology; this would prove that the conjecture stated above holds over the field [Formula: see text].

Full Text

Duke Authors

Cited Authors

  • Baldwin, JA; Levine, AS; Sarkar, S

Published Date

  • February 2017

Published In

Volume / Issue

  • 26 / 02

Start / End Page

  • 1740004 - 1740004

Published By

Electronic International Standard Serial Number (EISSN)

  • 1793-6527

International Standard Serial Number (ISSN)

  • 0218-2165

Digital Object Identifier (DOI)

  • 10.1142/s0218216517400041

Language

  • en