A NEW DISTINGUISHED FORM FOR 3-BRAIDS
Emille Davie Lawrence · Institutional Repositories DataBase (IRDB) · 2014
We show that every $3$-strand braid has a representative word of a given form, and furthermore, this form allows us, in most cases, to deduce positivity (or negativity) in the $\\sigma$-ordering of $B_{3}$. The $\\sigma$-ordering of $B_{n}$ was introduced by Patrick Dehornoy in the late 1990's, however, other (equivalent) orderings were discovered soon after by Fenn, Greene, Rolfsen, et al.