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2 results

  • Computable bounds for Rasmussen’s concordance invariant

  • Part of
  • Andrew Lobb
  • Journal:
    Compositio Mathematica / Volume 147 / Issue 2 / March 2011
    Published online by Cambridge University Press:
    13 December 2010, pp. 661-668
    Print publication:
    March 2011
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  • Given a diagram D of a knot K, we give easily computable bounds for Rasmussen’s concordance invariant s(K). The bounds are not independent of the diagram D chosen, but we show that for diagrams satisfying a given condition the bounds are tight. As a corollary we improve on previously known Bennequin-type bounds on the slice genus.

  • Categorification of the Colored Jones Polynomial and Rasmussen Invariant of Links

  • Anna Beliakova, Stephan Wehrli
  • Journal:
    Canadian Journal of Mathematics / Volume 60 / Issue 6 / 01 December 2008
    Published online by Cambridge University Press:
    20 November 2018, pp. 1240-1266
    Print publication:
    01 December 2008
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  • 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 Levine–Tristram signature.