Abstract
For a knot , let be the minimum length of an –stranded braid representative of . Fixing a knot , can be viewed as a function of , which we denote by . Examples of knots exist for which is a nonincreasing function. We investigate the behavior of , developing bounds on the function in terms of the genus of . The bounds lead to the conclusion that for any knot the function is eventually stable. We study the stable behavior of , with stronger results for homogeneous knots. For knots of nine or fewer crossings, we show that is stable on all of its domain and determine the function completely.
Citation
Cornelia Van Cott. "Relationships between braid length and the number of braid strands." Algebr. Geom. Topol. 7 (1) 181 - 196, 2007. https://doi.org/10.2140/agt.2007.7.181
Information