The almost alternating diagrams of the trivial knot |
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Authors: | Tsukamoto Tatsuya |
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Institution: | Department of Mathematics, Osaka Institute of Technology, Asahi, Osaka 535-8585, Japan, tsukamoto@ge.oit.ac.jp |
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Abstract: | Bankwitz characterized the alternating diagrams of the trivialknot. A non-alternating diagram is called almost alternatingif one crossing change makes the diagram alternating. We characterizethe almost alternating diagrams of the trivial knot. As a corollary,we determine the unknotting number one alternating knots withthe property that the unknotting operation can be done on itsalternating diagram. Received July 3, 2007. Revised September 29, 2008. |
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