2 citations · 4 across the 6 of their papers we have counts for
10 papers
A classification of rational 3-tangles
Bo-hyun Kwon
In this paper, we define the \textit{normal form} and \textit{normal coordinate} of a rational 3-tangle with respect to , where is the fixed two punctured d…
Normal forms for rational 3-tangles
Bo-hyun Kwon, Jung Hoon Lee
In this paper, we define the \textit{normal form} of collections of disjoint three \textit{bridge arcs} for a given rational -tangle. We show that there is a sequence of \textit…
On detecting the trivial rational -tangle
Bo-hyun Kwon
An important issue in classifying the rational -tangle is how to know whether or not the given tangle is the trivial rational 3-tangle called -tangle. The author\cite{1}…
On weak reducing disks for the unknot in -bridge position
Bo-Hyun Kwon, Jung Hoon Lee
We show that the complex of weak reducing disks for the unknot in -bridge position is contractible.
On the classification of a large set of rational 3-tangle diagrams
Bo-hyun Kwon
We note that a rational -tangle diagram is obtained from a combination of four generators. There is an algorithm to distinguish two rational -tangle diagrams up to isotopy. H…
An algorithm to classify rational 3-tangles
Bo-hyun Kwon
A - is the disjoint union of properly embedded arcs in the unit 3-ball; it is called rational if there is a homeomorphism of pairs from to $(D^2\times…
Rectangle condition and its applications
Bo-hyun Kwon
In this paper, we define the rectangle condition on the bridge sphere for a -bridge decomposition of a knot whose definition is analogous to the definition of the rectangle cond…
Uniqueness of reduced alternating rational 3-tangles
Bo-hyun Kwon
In this paper, We introduce an invariant of rational n-tangles which is obtained from the Kauffman bracket. It forms a vector with Laurent polynomial entries. We prove that the inv…
On the Jones polynomial of 2n-plat presentations of knots
Bo-hyun Kwon
In this paper, a method is given to calculate the Jones polynomial of the 6-plat presentations of knots by using a representation of the braid group into a group of…
On the HOMFLY polynomial of 4-plat presentations of knots
Bo-hyun Kwon
In this paper, I give a method to calculate the HOMFLY polynomials of knots by using a representation of the braid group B4 into a group of 3 ? 3 matrices. Also, I will give exampl…