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Knots with unknotting number one and Heegaard Floer homology |
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| Authors: | Peter Ozsváth Zoltán Szabó |
| Institution: | a Department of Mathematics, Columbia University, New York 10025, USA b Institute for Advanced Study, Princeton, New Jersey 08540, USA c Department of Mathematics, Princeton University, New Jersey 08544, USA |
| 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. |
| Keywords: | Alternating knots Unknotting number one Floer homology Goeritz matrix |
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