ABSTRACT
Some braid recognition algorithms have been constructed. The first of them was contained in the original work of Emil Artin. This chapter describes a geometrically explicit algorithm and the algebraic algorithm by Dehornoy. It presents a result by M. Berger concerning the minimal braid-word in Br representing the given braid isotopy class. Some generalisations of the invariant, such as the spherical and cylindrical braid group invariant, are also complete. The key point of completeness is that these invariants originate from some curves, and the braid can be uniquely restored from these curves. Another algorithm for braid recognition is purely algebraic. It was proposed by French mathematician Patrick Dehornoy. The chapter explains an algorithm that transforms each braid word to an equivalent one that is either unity or positive or negative.
