2021/04/20 by Yin Li, Li, Yin
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.SG
paper · pdf · doi:10.48550/arxiv.2104.10050
25 pages, 2 figures. v5: the main result has been further generalized to exclude exact Lagrangian K(π,1) spaces. An appendix discussing central units in group rings has been added. To appear in JSG
openalex publication_date 2021/04/20 · openalex created_date 2021/04/26 · arxiv created 2021/12/15 · arxiv updated 2021/12/16 · openalex updated_date 2026/07/28
Let M⊂ℂn+1 be a smooth affine hypersurface defined by the equation xy+p(z1,⋯,zn-1)=1, where p is a Brieskorn-Pham polynomial and n≥2. We prove that if L⊂ M is an orientable exact Lagrangian submanifold, then L does not admit a Riemannian metric with non-positive sectional curvature. The key point of the proof is to establish a version of homological mirror symmetry for the wrapped Fukaya category of M, from which the finite-dimensionality of the symplectic cohomology group SH0(M) follows by a Hochschild cohomology computation.