On The Augmentation Categories of Positive Braid Closures

Abstract

In this paper we show that 0-resolution of a crossing in the Legendrian closure of a positive braid induces a cohomologically faithful $A_{\infty }$ functor on augmentation categories. In particular, we compute the bilinearized Legendrian contact cohomology of these knots for augmentations induced by 0-resolution.

arXiv comment11 pages, 2 figures