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Span of the Jones polynomial of an alternating virtual link | Naoko Kamada
; | Date: |
3 Dec 2004 | Journal: | Algebr. Geom. Topol. 4 (2004) 1083-1101 | Subject: | Geometric Topology MSC-class: 57M25, 57M27 | math.GT | 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. | Source: | arXiv, math.GT/0412074 | Services: | Forum | Review | PDF | Favorites |
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