Knots with unknotting number one and Heegaard Floer homology

Research output: Contribution to journalArticle

35 Scopus citations

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 10 crossings and unknotting number equal to one.

Original languageEnglish (US)
Pages (from-to)705-745
Number of pages41
JournalTopology
Volume44
Issue number4
DOIs
StatePublished - Jul 1 2005

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Keywords

  • Alternating knots
  • Floer homology
  • Goeritz matrix
  • Unknotting number one

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