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Knot Floer Homology of (1, 1)-Knots

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Tokyo University of Agriculture and Technology, Koganei, Tokyo, 184-8588, Japan

    Hiroshi Goda & Takayuki Morifuji

  2. Department of Mathematics, Graduate School of Sciences, Hiroshima University, Hiroshima, 739-8526, Japan

    Hiroshi Matsuda

Authors
  1. Hiroshi Goda
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  2. Hiroshi Matsuda
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  3. Takayuki Morifuji
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Correspondence to Hiroshi Goda.

Additional information

Mathematics Subject Classiffications (2000). 57M27, 57M25

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Goda, H., Matsuda, H. & Morifuji, T. Knot Floer Homology of (1, 1)-Knots. Geom Dedicata 112, 197–214 (2005). https://doi.org/10.1007/s10711-004-5403-2

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  • DOI: https://doi.org/10.1007/s10711-004-5403-2

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