A type I move (conjugation) takes A B->B A for A, B element B_n where B_n is a braid group. A type II move (stabilization) takes A->A b_n or A->A b_n^(-1) for A element B_n, and b_n, A b_n, and A b_n^(-1) element B_(n + 1).

braid group | conjugation | knot move | Reidemeister moves | stabilization

Andrey Markov