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arxiv: math/0605018 · v2 · pith:VYIPCI3Mnew · submitted 2006-04-30 · 🧮 math.GT

The almost alternating diagrams of the trivial knot

classification 🧮 math.GT
keywords alternatingdiagramknotalmosttrivialrepresentingunknottingalternaing
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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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