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Journal of Topology 2009 2(1):77-104; doi:10.1112/jtopol/jtp001
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© 2009 London Mathematical Society

The almost alternating diagrams of the trivial knot

Tatsuya Tsukamoto

Department of Mathematics, Osaka Institute of Technology, Asahi, Osaka 535-8585, Japan, tsukamoto@ge.oit.ac.jp


  Abstract

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

Received July 3, 2007. Revised September 29, 2008.

2000 Mathematics Subject Classification 57M25

Dedicated to Professor Akio Kawauchi on his 60th birthday


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