A polynomial invariant of virtual knots

Cheng, Zhiyun

doi:10.1090/S0002-9939-2013-11785-5

A polynomial invariant of virtual knots
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by Zhiyun Cheng PDF

Proc. Amer. Math. Soc. 142 (2014), 713-725 Request permission

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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