2025/05/18 by Mohammed Abouzaid, Abouzaid, Mohammed, Daniel Álvarez‐Gavela +5 · 1 citation
Mathematics · #53D12 #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2505.12515
openalex publication_date 2025/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let L and M be closed, connected, smooth manifolds and let L \hookrightarrow T^*M be an exact Lagrangian embedding. The induced map L → M is known by earlier work to be a homotopy equivalence. We show that the associated normal invariant M → G/O factors through a map B(T,Q) → G/O which is a twisted version of the Waldhausen derivative T → G on the space T of tubes. Further, we show that this twisted derivative map itself factors though a map B(G/O) → G/O which is a twisted version of the S-duality map BG → G. In particular we deduce that the normal invariant of the homotopy equivalence L → M is 2-torsion.