67 research outputs found
Span of the Jones polynomial of an alternating virtual link
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.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-46.abs.htm
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