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2004 Span of the Jones polynomial of an alternating virtual link
Naoko Kamada
Algebr. Geom. Topol. 4(2): 1083-1101 (2004). DOI: 10.2140/agt.2004.4.1083


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. "Span of the Jones polynomial of an alternating virtual link." Algebr. Geom. Topol. 4 (2) 1083 - 1101, 2004.


Received: 4 March 2004; Revised: 24 October 2004; Accepted: 3 November 2004; Published: 2004
First available in Project Euclid: 21 December 2017

zbMATH: 1066.57018
MathSciNet: MR2100692
Digital Object Identifier: 10.2140/agt.2004.4.1083

Primary: 57M25
Secondary: 57M27

Rights: Copyright © 2004 Mathematical Sciences Publishers


Vol.4 • No. 2 • 2004
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