Algebraic and Geometric Topology 4 (2004),
paper no. 46, pages 1083-1101.
Span of the Jones polynomial of an alternating virtual link
Naoko Kamada
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.
Keywords.
Virtual knot theory, knot theory
AMS subject classification.
Primary: 57M25.
Secondary: 57M27.
DOI: 10.2140/agt.2004.4.1083
E-print: arXiv:math.GT/0412074
Submitted: 4 March 2004.
(Revised: 24 October 2004.)
Accepted: 3 November 2004.
Published: 21 November 2004.
Notes on file formats
Naoko Kamada
Department of Mathematics, Osaka City University, Sugimoto, Sumiyoshi-ku
Osaka, 558-8585, Japan
Email: naoko@sci.osaka-cu.ac.jp
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