Braid-positive Legendrian links

Abstract

Any link that is the closure of a positive braid has a natural Legendrian representative. These representatives were introduced in an earlier paper, where their Chekanov-Eliashberg contact homology was also evaluated. In this paper, we rephrase and improve that computation using a matrix representation. In particular, we present a way of finding all augmentations of such Legendrians, construct an augmentation which is also a ruling, and find surprising links to LU-decompositions and Gröbner bases.