Essential tori in link complements: impossibility of detecting the satellite structure by monotonic simplification

Details Essential tori in link complements: impossibility of detecting the satellite structure by monotonic simplification Essential tori in link complements: impossibility of detecting the satellite structure by monotonic simplification

2010-05-28

arxiv.org/abs/1005.5263v2

Mathematics

Geometric Topology

10 pages, 9 figures

Scientific paper

In a recent work "Arc-presentation of links: Monotonic simplification" Ivan Dynnikov showed 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.

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