Knot Floer Homology of (1, 1)-Knots

By H. Goda, H. Matsuda, Takayuki Morifuji. 2003

50 citations recorded by the source corpus.

We present a combinatorial method for a calculation of the knot Floer homology of (1, l)-knots, and then demonstrate it for nonalternating (1, 1)-knots with 10 crossings and the pretzel knots of type (−2,m, n). Our calculations determine the unknotting numbers and 4-genera of the pretzel knots of this type.

Subfields: Geometry and Topology, Mathematical Physics, Neurology

View Paper: https://www.semanticscholar.org/paper/b2e9bef48483473537058f0115db8b04be5feb26

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Citations in the corpus

Khovanov homology and the slice genus (2004, result): “Combining the results of [ 6 , 13, 15, 16], and [17] with some unpublished computations of the author, it appears that the value of τ has been determined for all but two knots of 10 crossings and fewer.”
The Ozsváth-Szabó and Rasmussen Concordance Invariants are not Equal (2005, methodology): “mology groups of a speciﬁc twisted Whitehead double which happens to be a (1,1) knot. A general technique for calculating the Floer homology of such knots was developed by Goda, Morifuji, and Matsuda [5] and we apply their technique here. We then use results of Eftekhary [4] for the 0-twisted Whiteh”
On Floer homology and the Berge conjecture on knots admitting lens space surgeries (2007, background): “S(3) are precisely those knots admitting a genus one Heegaard diagram (note that [11] refers to one-bridge knots as (1, 1) knots).”
On knot Floer homology and cabling (2004, background): “AMS Classification 57M27; 57R58 Keywords Knots, Floer homology, cable, satellite, Heegaard diagrams”