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arXiv · 1005.5263

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

Alexandr Kazantsev
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Abstract

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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Alexandr Kazantsev. 2010-10-04. Essential tori in link complements: impossibility of detecting the satellite structure by monotonic simplification. https://arxiv.org/abs/1005.5263

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