Computations of heegaard-floer knot homology Article

Baldwin, JA, Gillam, WD. (2012). Computations of heegaard-floer knot homology . Journal of Knot Theory and its Ramifications, 21(8), 10.1142/S0218216512500757

cited authors

  • Baldwin, JA; Gillam, WD

abstract

  • We compute the knot Floer homology of knots with at most 12 crossings, as well as the τ invariant for knots with at most 11 crossings, using the combinatorial approach described by Manolescu, Ozsváth and Sarkar. We review their construction, giving two examples that can be workout out by hand, and we explain some ideas we used to simplify the computation. We conclude with a discussion of knot Floer homology for small knots, and we formulate a conjecture about the behavior of knot Floer homology under mutation, paying especially close attention to the KinoshitaTerasaka knot and its Conway mutant. Finally, we discuss a conjecture of Rasmussen on relationship between Khovanov homology and knot Floer homology, and observe that it is consistent with our calculations. © 2012 World Scientific Publishing Company.

authors

publication date

  • July 1, 2012

published in

Digital Object Identifier (DOI)

volume

  • 21

issue

  • 8