The almost alternating diagrams of the trivial knot

Details The almost alternating diagrams of the trivial knot The almost alternating diagrams of the trivial knot

2006-04-30

arxiv.org/abs/math/0605018v2

Mathematics

Geometric Topology

29 pages, 18 figures

Scientific paper

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.

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