by S.Yu. Orevkov

Let $B_m=\langle\sigma_1,\dots,\sigma_m\,|\, \sigma_j\sigma_{j+1}\sigma_j =\sigma_{j+1}\sigma_j\sigma_{j+1}$, $[\sigma_j,\sigma_k]=1$ for $|k-j|>1\rangle$ be the braid group. A braid $b$ is called quasipositive if it has the form $b=(a_1\sigma_1a_1^{-1})\dots(a_k\sigma_1a_k^{-1})$. Using Gromov's theory of pseudo holomorphic curves, we prove that $b\in B_m$ is quasipositive if and only if $b\sigma_m\in B_{m+1}$ is quasipositive.