Geometriae Dedicata

, Volume 112, Issue 1, pp 197–214

Knot Floer Homology of (1, 1)-Knots

Article

DOI: 10.1007/s10711-004-5403-2

Cite this article as:
Goda, H., Matsuda, H. & Morifuji, T. Geom Dedicata (2005) 112: 197. doi:10.1007/s10711-004-5403-2

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.

Keywords

Knot Floer homologyFloer homology(1, 1)-knotstunnel number one knotsPretzel knot

Copyright information

© Springer 2005

Authors and Affiliations

  • Hiroshi Goda
    • 1
  • Hiroshi Matsuda
    • 2
  • Takayuki Morifuji
    • 1
  1. 1.Department of MathematicsTokyo University of Agriculture and TechnologyTokyoJapan
  2. 2.Department of Mathematics, Graduate School of SciencesHiroshima UniversityHiroshimaJapan