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November 2007 An index of an enhanced state of a virtual link diagram
Naoko Kamada
Hiroshima Math. J. 37(3): 409-429 (November 2007). DOI: 10.32917/hmj/1200529811


We construct a polynomial invariant of a virtual magnetic graph diagram by defining an index of an enhanced state. For a virtual link diagram, it equals the Miyazawa polynomial and then the maximal degree on $t$ of the polynomials not only gives a lower bound of the real crossing number but also that of the virtual crossing number. Moreover, by definition we can calculate the polynomial for a link in a thickened surface or a Gauss chord diagram directly without transforming it into a virtual link diagram.


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Naoko Kamada. "An index of an enhanced state of a virtual link diagram." Hiroshima Math. J. 37 (3) 409 - 429, November 2007.


Published: November 2007
First available in Project Euclid: 17 January 2008

zbMATH: 1146.57017
MathSciNet: MR2376727
Digital Object Identifier: 10.32917/hmj/1200529811

Primary: 57M25
Secondary: 57M27

Rights: Copyright © 2007 Hiroshima University, Mathematics Program


Vol.37 • No. 3 • November 2007
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