2024/11/13 by Johan Asplund, Asplund, Johan, Yash Deshmukh +3 · 2 citations
Mathematics · Physics and Astronomy · #53D12 #53D37 #55P42 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2411.08841
openalex publication_date 2024/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
Let R be a commutative ring spectrum. We construct the wrapped Donaldson--Fukaya category with coefficients in R of any stably polarized Liouville sector. We show that any two R-orientable and isomorphic objects admit R-orientations so that their R-fundamental classes coincide. Our main result is that any closed exact Lagrangian R-brane in the cotangent bundle of a closed manifold is isomorphic to an R-brane structure on the zero section in the wrapped Donaldson--Fukaya category, generalizing a well-known result over the integers. To achieve this, we prove that the Floer homotopy type of the cotangent fiber is given by the stable homotopy type of the based loop space of the zero section.