Two-fold quasi-alternating links, Khovanov homology and instanton homology

Christopher Scaduto, Matthew Stoffregen

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We introduce a class of links strictly containing quasi-alternating links for which mod 2 reduced Khovanov homology is always thin. We compute the framed instanton homology for double branched covers of such links. Aligning certain dotted markings on a link with bundle data over the branched cover, we also provide many computations of framed instanton homology in the presence of a non-trivial real 3-plane bundle. We discuss evidence for a spectral sequence from the twisted Khovanov homology of a link with mod 2 coefficients to the framed instanton homology of the double branched cover. We also discuss the relevant mod 4 gradings.

Original languageEnglish (US)
Pages (from-to)167-205
Number of pages39
JournalQuantum Topology
Volume9
Issue number1
DOIs
StatePublished - 2018
Externally publishedYes

Keywords

  • Instanton homology
  • Khovanov homology
  • Knots
  • Quasi-alternating

ASJC Scopus subject areas

  • Mathematical Physics
  • Geometry and Topology

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