2019/07/22 by Yin Li, Li, Yin
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1907.09257
openalex publication_date 2019/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An exact Calabi-Yau structure, originally introduced by Keller, is a special kind of smooth Calabi-Yau structure in the sense of Kontsevich-Vlassopoulos. For a Weinstein manifold M, the existence of an exact Calabi-Yau structure on the wrapped Fukaya category W(M) imposes strong restrictions on its symplectic topology. Under the cyclic open-closed map constructed by Ganatra, an exact Calabi-Yau structure on W(M) induces a class b in the degree one equivariant symplectic cohomology SHS11(M). Any Weinstein manifold admitting a quasi-dilation in the sense of Seidel-Solomon has an exact Calabi-Yau structure on W(M). We prove that there are many Weinstein manifolds whose wrapped Fukaya categories are exact Calabi-Yau despite the fact the fact there is no quasi-dilation in SH1(M), a typical example is given by the affine hypersurface \x3+y3+z3+w3=1\⊂ℂ4. As an application, we prove the homological essentiality of Lagrangian spheres in many odd-dimensional smooth affine varieties with exact Calabi-Yau wrapped Fukaya categories.