A note on the writhe polynomial and the virtual crossing number

Abstract

In this note we give a new lower bound on the virtual crossing number via the writhe polynomial, which refines a result of B. Mellor. The proof is based on a new interpretation of the writhe polynomial. The characterization of the writhe polynomial is also discussed.

arXiv commentThe main result of this paper has been obtained by S. Satoh and K. Taniguchi in "The writhes of a virtual knot", Fundamenta Mathematicae 225 (2014), no. 1,327--342