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The almost alternating diagrams of the trivial knot

Geometric Topology 2014-02-26 v2

Abstract

Bankwitz characterized an alternating diagram representing the trivial knot. A non-alternating diagram is called almost alternating if one crossing change makes the diagram alternating. We characterize an almost alternaing diagram representing the trivial knot. As a corollary we determine an unknotting number one alternating knot with a property that the unknotting operation can be done on its alternating diagram.

Keywords

Cite

@article{arxiv.math/0605018,
  title  = {The almost alternating diagrams of the trivial knot},
  author = {Tatsuya Tsukamoto},
  journal= {arXiv preprint arXiv:math/0605018},
  year   = {2014}
}

Comments

29 pages, 18 figures