Isomorphism in the augmentation category

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Authors: Honghao Gao, Hanming Liu
Cited by: 0

Abstract

Given a Legendrian submanifold in any dimension, we prove that two augmentations are isomorphic within the positive augmentation category exactly when they differ by a combination of a dga homotopy and a dilation. This extends the corresponding statement for Legendrian knots and links, but instead of relying on the dga for consistent copies, we make use of quantum flow tree techniques. Consequently, we can strengthen and clarify a result of the first author as follows: for knot contact homology, the augmentation category is not in general equivalent to the microlocal rank 1 sheaf category.

Fields of Study & Subjects

Geometric and Algebraic Topology Homotopy and Cohomology in Algebraic Topology Algebraic Geometry and Number Theory

Publication details

Journal / source
arXiv (Cornell University)
Publication date
13 February 2026
Language
EN
Document type
Preprint