2025/06/06 by Sylvain Courte, Courte, Sylvain, Noah Porcelli +1
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2506.06110
openalex publication_date 2025/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
Motivated by the strong nearby Lagrangian conjecture, we constrain the parametrised Whitehead torsion of a family of closed exact Lagrangian submanifolds in a cotangent bundle. We prove the parametrised Whitehead torsion admits a factorisation through simpler maps, in particular implying it is trivial on π0, π1, and that its image is divisible by the Euler characteristic. We provide concrete implications for the Lagrangian monodromy question in the case of a high dimensional torus. This generalises earlier work of Abouzaid and Kragh \citeAbKr on the π0 version, using different methods. Our main tool is the theory of twisted generating functions, building on \citeACGK.