Knots with unknotting number one and Heegaard Floer homology
By Peter S. Ozsv'ath, Zolt'an Szab'o. 2004
71 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Neurology
View Paper: https://www.semanticscholar.org/paper/026bf03f1ba39b84cf6f2396848ee7e00f8bdf1d
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In Computational Theory and Mathematics
- A. Stipsicz
- Ciprian Manolescu
- Peter S. Ozsv'ath
- Zolt'an Szab'o
- Brendan Owens
- Jennifer Hom
- M. Hedden
- Jacob Rasmussen
In Geometry and Topology
- A. Stipsicz
- Ciprian Manolescu
- Peter S. Ozsv'ath
- Zolt'an Szab'o
- Ian Zemke
- Jennifer Hom
- John A. Baldwin
- M. Hedden
In Neurology
- A. Stipsicz
- Peter S. Ozsv'ath
- Ciprian Manolescu
- Zolt'an Szab'o
- M. Hedden
- Brendan Owens
- Ian Zemke
- Jennifer Hom
Citations in the corpus
- Knot Floer homology and rational surgeries (2005, background): “This new knot C is obtained by performing the unknotting operation, but connecting the two strands which were crossed by an arc ; C then is the branched double-cover , compare [23].”
- A concordance invariant from the Floer homology of double branched covers (2005, methodology): “In another direction, we used the method of Ozsváth and Szabó from [29] to compute δ for several H-thin knots of a special form.”
- Grid Homology for Knots and Links (2015, methodology): “For example, Heegaard Floer homology can be used to study unknotting numbers of knots [176].”