Constructing doubly-pointed Heegaard diagrams compatible with (1,1) knots

  title={Constructing doubly-pointed Heegaard diagrams compatible with (1,1) knots},
  author={Philip Ording},
  journal={arXiv: Geometric Topology},
  • Philip Ording
  • Published 25 October 2011
  • Mathematics
  • arXiv: Geometric Topology
A (1,1) knot K in a 3-manifold M is a knot that intersects each solid torus of a genus 1 Heegaard splitting of M in a single trivial arc. Choi and Ko developed a parameterization of this family of knots by a four-tuple of integers, which they call Schubert's normal form. This article presents an algorithm for constructing a doubly-pointed Heegaard diagram compatible with K, given a Schubert's normal form for K. The construction, coupled with results of Ozsv\'ath and Szab\'o, provides a… 


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