The almost alternating diagrams of the trivial knot

Tatsuya Tsukamoto

doi:10.1112/jtopol/jtp001

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The almost alternating diagrams of the trivial knot

Tatsuya Tsukamoto

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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.

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Tatsuya Tsukamoto. 2006-07-14. The almost alternating diagrams of the trivial knot. https://doi.org/10.1112/jtopol%2Fjtp001

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