Knots with unknotting number one and Heegaard Floer homology

2004/01/30 by Peter Ozsvath, Ozsvath, Peter, Zoltan Szabo +1 · 1 citation
Mathematics · #53D40 #57M27 #57R58 #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG) #math.GT #math.SG #msc:53D40 #msc:57M27 #msc:57R58

paper · pdf · doi:10.48550/arxiv.math/0401426

Minor revisions, updated references

arxiv created 2005/03/15 · arxiv updated 2009/12/01

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.

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