Positive microlocal holonomies are globally regular
Abstract
We establish a geometric criterion for local microlocal holonomies to be globally regular on the moduli space of Lagrangian fillings. This local-to-global regularity result holds for arbitrary Legendrian links and it is a key input for the study of cluster structures on such moduli spaces. Specifically, we construct regular functions on derived moduli stacks of sheaves with Legendrian microsupport by studying the Hochschild homology of the associated dg-categories via relative Lagrangian skeleta. In this construction, a key geometric result is that local microlocal merodromies along positive relative cycles in Lagrangian fillings yield global Hochschild 0-cycles for these dg-categories.
Fields of Study & Subjects
Advanced Topics in Algebra
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- Communications of the American Mathematical Society
- Volume
- 6
- Issue
- 9
- Pages
- 492–535
- Publication date
- 24 April 2026
- Language
- EN