Making use of the Nielsen fixed point theory, we study a conjugacy invariant of braids, which we call the level index function. We present a simple algorithm for computing it for positive permutation cyclic braids.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm216-2-4,
author = {Micha\l\ Misiurewicz and Ana Rodrigues},
title = {Fixed points for positive permutation braids},
journal = {Fundamenta Mathematicae},
volume = {219},
year = {2012},
pages = {129-146},
zbl = {1256.57015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm216-2-4}
}
Michał Misiurewicz; Ana Rodrigues. Fixed points for positive permutation braids. Fundamenta Mathematicae, Tome 219 (2012) pp. 129-146. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm216-2-4/