Kauffman introduced a fundamental invariant of a virtual knot called the odd writhe. There are several generalizations of the odd writhe, such as the index polynomial and the odd writhe polynomial. In this paper, we define the n-writhe for each non-zero integer n, which unifies these invariants, and study various properties of the n-writhe.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm225-1-15,
author = {Shin Satoh and Kenta Taniguchi},
title = {The writhes of a virtual knot},
journal = {Fundamenta Mathematicae},
volume = {227},
year = {2014},
pages = {327-341},
zbl = {1302.57033},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm225-1-15}
}
Shin Satoh; Kenta Taniguchi. The writhes of a virtual knot. Fundamenta Mathematicae, Tome 227 (2014) pp. 327-341. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm225-1-15/