2017/02/11 by Hiro Lee Tanaka, Li-Sheng Tseng · 1 citation
Mathematics · #math.SG #math.AT #math.DG
paper · pdf · doi:10.4310/cjm.2018.v6.n3.a1
published as Cambridge Journal of Mathematics (2018), 213--266
arxiv created 2017/02/11 · arxiv updated 2020/03/12
Recently, Tsai-Tseng-Yau constructed new invariants of symplectic manifolds: a sequence of Aoo-algebras built of differential forms on the symplectic manifold. We show that these symplectic Aoo-algebras have a simple topological interpretation. Namely, when the cohomology class of the symplectic form is integral, these Aoo-algebras are equivalent to the standard de Rham differential graded algebra on certain odd-dimensional sphere bundles over the symplectic manifold. From this equivalence, we deduce for a closed symplectic manifold that Tsai-Tseng-Yau's symplectic Aoo-algebras satisfy the Calabi-Yau property, and importantly, that they can be used to define an intersection theory for coisotropic/isotropic chains. We further demonstrate that these symplectic Aoo-algebras satisfy several functorial properties and lay the groundwork for addressing Weinstein functoriality and invariance in the smooth category.