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A polynomial invariant of virtual knots


Author: Zhiyun Cheng
Journal: Proc. Amer. Math. Soc. 142 (2014), 713-725
MSC (2010): Primary 57M25
DOI: https://doi.org/10.1090/S0002-9939-2013-11785-5
Published electronically: November 6, 2013
MathSciNet review: 3134011
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Abstract: The aim of this paper is to introduce a polynomial invariant $ f_K(t)$ for virtual knots. We show that $ f_K(t)$ can be used to distinguish some virtual knot from its inverse and mirror image. The behavior of $ f_K(t)$ under a connected sum is also given. Finally, we discuss which kinds of polynomials can be realized as $ f_K(t)$ for some virtual knot $ K$.


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Additional Information

Zhiyun Cheng
Affiliation: School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People’s Republic of China
Email: czy@mail.bnu.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-2013-11785-5
Keywords: Virtual knot, odd writhe polynomial
Received by editor(s): March 4, 2012
Received by editor(s) in revised form: March 28, 2012
Published electronically: November 6, 2013
Additional Notes: The author was supported by NSF 11171025
Communicated by: Kevin Whyte
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.