Stepan Yu Orevkov

Markov moves for quasipositive braids

Abstract Let B m =〈σ 1 ,…,σ m | σ j σ j+1 σ j =σ j+1 σ j σ j+1 , [σj,σk]=1 for |k−j|>1〉 be the braid group. A braid b is called quasipositive if it has the form b=(a1σ1a1−1)⋯(akσ1ak−1) . Using Gromovs theory of pseudo holomorphic curves, we prove that b∈Bm is quasipositive if and only if bσm∈Bm+1 is quasipositive.