Geodesic
Span of the Jones polynomial of an alternating virtual link
Kamada, Naoko1
1Department of Mathematics, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan
Algebraic and Geometric Topology, Tome 4 (2004) no. 2, pp. 1083-1101
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For an oriented virtual link, L H Kauffman defined the f–polynomial (Jones polynomial). The supporting genus of a virtual link diagram is the minimal genus of a surface in which the diagram can be embedded. In this paper we show that the span of the f–polynomial of an alternating virtual link L is determined by the number of crossings of any alternating diagram of L and the supporting genus of the diagram. It is a generalization of Kauffman–Murasugi–Thistlethwaite’s theorem. We also prove a similar result for a virtual link diagram that is obtained from an alternating virtual link diagram by virtualizing one real crossing. As a consequence, such a diagram is not equivalent to a classical link diagram.

DOI : 10.2140/agt.2004.4.1083
Keywords: virtual knot theory, knot theory

Kamada, Naoko  1

1 Department of Mathematics, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan 
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Kamada, Naoko. Span of the Jones polynomial of an alternating virtual link. Algebraic and Geometric Topology, Tome 4 (2004) no. 2, pp. 1083-1101. doi: 10.2140/agt.2004.4.1083

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