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/