English

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

Geometric Topology 2010-10-05 v2

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.

Keywords

Cite

@article{arxiv.1005.5263,
  title  = {Essential tori in link complements: impossibility of detecting the satellite structure by monotonic simplification},
  author = {Alexandr Kazantsev},
  journal= {arXiv preprint arXiv:1005.5263},
  year   = {2010}
}

Comments

10 pages, 9 figures