A polynomial invariant of virtual knots

By Zhiyun Cheng. 2012

55 citations recorded by the source corpus.

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 connected sum is also given. Finally we discuss which kind of polynomial can be realized as $f_K(t)$ for some virtual knot $K$.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1c7ce853b27f4405ef742a89afeee6ad131cd65b

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In Discrete Mathematics and Combinatorics

1. Hongzhu Gao
2. Zhiyun Cheng

In Geometry and Topology

1. Hongzhu Gao
2. Zhiyun Cheng

In Mathematical Physics

1. Hongzhu Gao
2. Zhiyun Cheng

Citations in the corpus

• A polynomial invariant of virtual links (2013, methodology): “If k = 0, the invariance of the odd writhe polynomial has been proved in [1].”