Categorification of the colored jones polynomial and rasmussen invariant of links

Anna Beliakova, Stephan Wehrli

Research output: Contribution to journalArticle

22 Scopus citations

Abstract

We define a family of formal Khovanov brackets of a colored link depending on two parameters. The isomorphism classes of these brackets are invariants of framed colored links. The Bar-Natan functors applied to these brackets produce Khovanov and Lee homology theories categorifying the colored Jones polynomial. Further, we study conditions under which framed colored link cobordisms induce chain transformations between our formal brackets. We conjecture that for special choice of parameters, Khovanov and Lee homology theories of colored links are functorial (up to sign). Finally, we extend the Rasmussen invariant to links and give examples where this invariant is a stronger obstruction to sliceness than the multivariable Levinc-Tristram signature.

Original languageEnglish (US)
Pages (from-to)1240-1266
Number of pages27
JournalCanadian Journal of Mathematics
Volume60
Issue number6
DOIs
StatePublished - Dec 2008

Keywords

  • Colored jones polynomial
  • Framed cobordism
  • Khovanov homology
  • Movie moves
  • Slice genus

ASJC Scopus subject areas

  • Mathematics(all)

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