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ON THE PRESENTATION OF A LINK AS A SUM OF TWO DESCENDING TANGLE DIAGRAMS
Preview AbstractIn this paper, we define the notion of descending tangle diagrams and give a presentation of a link as a sum of two descending tangle diagrams. We also introduce a new invariant of links and find its basic properties.
On unknotting operations of rotation type
Preview AbstractAn unknotting operation is a local move on a knot diagram such that any knot diagram can be transformed into a diagram of the unknot by a finite sequence of the operations and Reidemeister moves. In this paper, we introduce a new local move H(T) on a knot diagram which is obtained by the rotation of a tangle diagram T and study their properties. As an application, we prove that the H(T)-move is an unknotting operation for any descending tangle diagram T.