Span of the Jones polynomial of an alternating virtual link

Naoko Kamada

doi:10.2140/agt.2004.4.1083

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arXiv · math/0412074

Span of the Jones polynomial of an alternating virtual link

Naoko Kamada

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Abstract

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.

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Naoko Kamada. 2004-12-03. Span of the Jones polynomial of an alternating virtual link. https://doi.org/10.2140/agt.2004.4.1083

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