AbstractSuppose that a knot is deformed into another knot by a ν-unknotting operation. Then we will show that the difference of their Nakanishi indices is less than or equal to three and that the difference of the minimum numbers of generators of the first homology groups of their double branched covers is less than or equal to two. We also give infinitely many examples of composite knots with ν-unknotting number one
We determine a class of knots, which includes unknotting number one knots, within which Khovanov hom...
We call a knot K a complete Alexander neighbor if every possible Alexander polynomial is realized by...
ABSTRACT. Let K (resp. L) be a Montesinos knot (resp. Iink) with at least four branches. Tben we sho...
AbstractSuppose that a knot is deformed into another knot by a ν-unknotting operation. Then we will ...
The unknotting number of a knot is the minimum number of crossings one must change to turn that knot...
AbstractBy using a result of L. Rudolph concerning the four-genus of a classical knot, we calculate ...
We introduce the Alexander–Beck module of a knot as a canonical refinement of the classical Alexande...
There is no known algorithm for determining whether a knot has unknotting number one, practical or o...
We prove for rational knots a conjecture of Adams et al. that an alternating unknotting number one k...
AbstractIntroducing a way to modify knots using n-trivial rational tangles, we show that knots with ...
We will discuss a technique to distinguish knots via an algebraic invariant, namely the Alexander mo...
example of a knot where the unknotting number was not realized in a minimal projection of the knot. ...
Abstract. Cochran defined the nth-order integral Alexander module of a knot in the three sphere as t...
AbstractLet K be an unknotting number one knot. By calculating Casson's invariant for the 2-fold bra...
We prove that if an alternating knot has unknotting number one, then there exists an unknotting cros...
We determine a class of knots, which includes unknotting number one knots, within which Khovanov hom...
We call a knot K a complete Alexander neighbor if every possible Alexander polynomial is realized by...
ABSTRACT. Let K (resp. L) be a Montesinos knot (resp. Iink) with at least four branches. Tben we sho...
AbstractSuppose that a knot is deformed into another knot by a ν-unknotting operation. Then we will ...
The unknotting number of a knot is the minimum number of crossings one must change to turn that knot...
AbstractBy using a result of L. Rudolph concerning the four-genus of a classical knot, we calculate ...
We introduce the Alexander–Beck module of a knot as a canonical refinement of the classical Alexande...
There is no known algorithm for determining whether a knot has unknotting number one, practical or o...
We prove for rational knots a conjecture of Adams et al. that an alternating unknotting number one k...
AbstractIntroducing a way to modify knots using n-trivial rational tangles, we show that knots with ...
We will discuss a technique to distinguish knots via an algebraic invariant, namely the Alexander mo...
example of a knot where the unknotting number was not realized in a minimal projection of the knot. ...
Abstract. Cochran defined the nth-order integral Alexander module of a knot in the three sphere as t...
AbstractLet K be an unknotting number one knot. By calculating Casson's invariant for the 2-fold bra...
We prove that if an alternating knot has unknotting number one, then there exists an unknotting cros...
We determine a class of knots, which includes unknotting number one knots, within which Khovanov hom...
We call a knot K a complete Alexander neighbor if every possible Alexander polynomial is realized by...
ABSTRACT. Let K (resp. L) be a Montesinos knot (resp. Iink) with at least four branches. Tben we sho...
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