English

Knots with unknotting number one and Heegaard Floer homology

Geometric Topology 2007-05-23 v2 Symplectic Geometry

Abstract

We use Heegaard Floer homology to give obstructions to unknotting a knot with a single crossing change. These restrictions are particularly useful in the case where the knot in question is alternating. As an example, we use them to classify all knots with crossing number less than or equal to nine and unknotting number equal to one. We also classify alternating knots with ten crossings and unknotting number equal to one.

Keywords

Cite

@article{arxiv.math/0401426,
  title  = {Knots with unknotting number one and Heegaard Floer homology},
  author = {Peter Ozsvath and Zoltan Szabo},
  journal= {arXiv preprint arXiv:math/0401426},
  year   = {2007}
}

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