Knots with unknotting number one and Heegaard Floer homology

Peter Ozsváth; Zoltán Szabó

doi:10.1016/j.top.2005.01.002

Knots with unknotting number one and Heegaard Floer homology

Peter Ozsváth, Zoltán Szabó

Mathematics

Research output: Contribution to journal › Article › peer-review

39 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 language	English (US)
Pages (from-to)	705-745
Number of pages	41
Journal	Topology
Volume	44
Issue number	4
DOIs	https://doi.org/10.1016/j.top.2005.01.002
State	Published - Jul 2005

All Science Journal Classification (ASJC) codes

Geometry and Topology

Keywords

Alternating knots
Floer homology
Goeritz matrix
Unknotting number one

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10.1016/j.top.2005.01.002

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title = "Knots with unknotting number one and Heegaard Floer homology",

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.",

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AU - Ozsváth, Peter

AU - Szabó, Zoltán

PY - 2005/7

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N2 - 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.

AB - 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.

KW - Alternating knots

KW - Floer homology

KW - Goeritz matrix

KW - Unknotting number one

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JO - Topology

JF - Topology

IS - 4

ER -

Knots with unknotting number one and Heegaard Floer homology

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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