2025/09/06 by Yonghwan Kim, Kim, Yonghwan · 1 voice
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.SG
paper · pdf · doi:10.48550/arxiv.2509.05856
60 pages, 13 figures; v2 minor changes, added references; v3 minor referee's corrections and bibliographic updates. This is the final version, to appear in Journal of Topology
openalex publication_date 2025/09/06 · arxiv published 2025/09/06 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28 · arxiv created 2026/08/01 · arxiv updated 2026/08/01
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 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.