AbstractWe 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
We define sutured Heegaard diagrams for null-homologous knots in 3–manifolds. These diagrams are use...
In mathematics, a knot is a single strand crossed over itself any number of times, and connected at ...
This paper explores the problem of unknotting closed braids and classical knots in mathematical knot...
We use Heegaard Floer homology to obtain bounds on unknotting numbers. This is a generalisation of O...
We prove that if an alternating knot has unknotting number one, then there exists an unknotting cros...
The unknotting number of a knot is the minimum number of crossings one must change to turn that knot...
For any knot with genus one and unknotting number one, other than the figure-eight knot, we prove th...
Abstract. We review the construction of Heegaard–Floer homology for closed three-manifolds and also ...
There is no known algorithm for determining whether a knot has unknotting number one, practical or o...
We use the knot filtration on the Heegaard Floer complex dCF to define an integer invariant (K) for ...
AbstractBy using a result of L. Rudolph concerning the four-genus of a classical knot, we calculate ...
The Heegaard Floer correction term (d-invariant) is an invariant of rational homology 3-spheres equi...
In an earlier paper, we introduced a knot invariant for a null-homologous knot K in an oriented thre...
We determine a class of knots, which includes unknotting number one knots, within which Khovanov hom...
The untwisting number of a knot K is the minimum number of null-homologous twists required to conver...
We define sutured Heegaard diagrams for null-homologous knots in 3–manifolds. These diagrams are use...
In mathematics, a knot is a single strand crossed over itself any number of times, and connected at ...
This paper explores the problem of unknotting closed braids and classical knots in mathematical knot...
We use Heegaard Floer homology to obtain bounds on unknotting numbers. This is a generalisation of O...
We prove that if an alternating knot has unknotting number one, then there exists an unknotting cros...
The unknotting number of a knot is the minimum number of crossings one must change to turn that knot...
For any knot with genus one and unknotting number one, other than the figure-eight knot, we prove th...
Abstract. We review the construction of Heegaard–Floer homology for closed three-manifolds and also ...
There is no known algorithm for determining whether a knot has unknotting number one, practical or o...
We use the knot filtration on the Heegaard Floer complex dCF to define an integer invariant (K) for ...
AbstractBy using a result of L. Rudolph concerning the four-genus of a classical knot, we calculate ...
The Heegaard Floer correction term (d-invariant) is an invariant of rational homology 3-spheres equi...
In an earlier paper, we introduced a knot invariant for a null-homologous knot K in an oriented thre...
We determine a class of knots, which includes unknotting number one knots, within which Khovanov hom...
The untwisting number of a knot K is the minimum number of null-homologous twists required to conver...
We define sutured Heegaard diagrams for null-homologous knots in 3–manifolds. These diagrams are use...
In mathematics, a knot is a single strand crossed over itself any number of times, and connected at ...
This paper explores the problem of unknotting closed braids and classical knots in mathematical knot...
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