  We study braid varieties and their relation to open positroid varieties. We
discuss four different types of braids associated to open positroid strata and
show that their associated Legendrian links are all Legendrian isotopic. In
particular, we prove that each open positroid stratum can be presented as the
augmentation variety for four different Legendrian fronts described in terms of
either permutations, juggling patterns, cyclic rank matrices or Le diagrams. We
also relate braid varieties to open Richardson varieties and brick manifolds,
showing that the latter provide projective compactifications of braid
varieties, with normal crossing divisors at infinity.
