THE PROBLEM OF DETECTING THE SATELLITE STRUCTURE OF A LINK BY MONOTONIC SIMPLIFICATION.

In a recent work "Arc-presentation of links: Monotonic simplification", Dynnikov shows that each rectangular diagram of the unknot, composite link, or split link can be monotonically simplified into a trivial, composite, or split diagram, respectively. The following natural question arises: Is it always possible to simplify monotonically a rectangular diagram of a satellite knot or link into one where the satellite structure is seen? Here we give a negative answer to that question both for knot and link cases. An example of a torus embedding that cannot be obtained from ordinary "thin" torus by methods of paper [2] is also constructed. [ABSTRACT FROM AUTHOR]