2019/10/02 by Oleg Lazarev, Lazarev, Oleg · 2 citations
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Symplectic Geometry (math.SG) #math.KT #math.SG
paper · pdf · doi:10.48550/arxiv.1910.01101
37 pages, 7 figures. Comments welcome!
arxiv created 2019/10/02 · openalex publication_date 2019/10/02 · arxiv updated 2019/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that geometric intersections between Weinstein handles induce algebraic relations in the wrapped Fukaya category, which we use to study the Grothendieck group. We produce a surjective map from middle-dimensional singular cohomology to the Grothendieck group, show that the geometric acceleration map to symplectic cohomology factors through the categorical Dennis trace map, and introduce a Viterbo functor for C0-close Weinstein hypersurfaces, which gives an obstruction for Legendrians to be C0-close. We show that symplectic flexibility is a geometric manifestation of Thomason's correspondence between split-generating subcategories and subgroups of the Grothendieck group, which we use to upgrade Abouzaid's split-generation criterion to a generation criterion for Weinstein domains. Thomason's theorem produces exotic presentations for certain categories and we give geometric analogs: exotic Weinstein presentations for standard cotangent bundles and Legendrians whose Chekanov-Eliashberg algebras are not quasi-isomorphic but are derived Morita equivalent.