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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the crossing numbers of a virtual knot


Authors: Shin Satoh and Yumi Tomiyama
Journal: Proc. Amer. Math. Soc. 140 (2012), 367-376
MSC (2010): Primary 57M25; Secondary 57M27
Published electronically: May 26, 2011
MathSciNet review: 2833547
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Abstract: We give lower bounds of the real crossing number of a virtual knot in terms of the Jones polynomial and the Miyazawa polynomial. As an application, we prove the existence of a virtual knot such that the real and virtual crossing numbers are equal to $ m$ and $ n$ for any positive integers $ m<n$.


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Additional Information

Shin Satoh
Affiliation: Department of Mathematics, Kobe University, Rokkodai-cho 1-1, Nada-ku, Kobe 657-0013, Japan
Email: shin@math.kobe-u.ac.jp

Yumi Tomiyama
Affiliation: Department of Mathematics, Kobe University, Rokkodai-cho 1-1, Nada-ku, Kobe 657-0013, Japan

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10917-1
PII: S 0002-9939(2011)10917-1
Keywords: Virtual knot, crossing number, Jones polynomial, Miyazawa polynomial, arrow polynomial.
Received by editor(s): March 25, 2010
Received by editor(s) in revised form: November 14, 2010
Published electronically: May 26, 2011
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.