Simple homotopy theory for Fukaya categories
Abstract
Abstract We develop a categorical framework for simple homotopy theory in Fukaya categories, based on the fundamental group of the ambient symplectic manifold. When the first Chern class vanishes, we show that any isomorphism in the Fukaya category of a Weinstein manifold has trivial Whitehead torsion. As an application, we prove that any pair of closed connected Lagrangians that are isomorphic in the Fukaya category of such a Weinstein manifolds are simple homotopy equivalent, provided one of the Lagrangians is homotopy equivalent to the ambient symplectic manifold and their fundamental groups are isomorphic.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Homotopy and Cohomology in Algebraic Topology
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Journal of Topology
- Volume
- 19
- Issue
- 3
- Publication date
- 27 August 2026
- Language
- EN