2020/08/24 by Jason DeVito, Fernando Galaz‐García, DeVito, Jason +3
Mathematics · Computer Science · #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2008.10278
Under mild topological restrictions, this article establishes that a smooth, closed, simply connected manifold of dimension at most seven which can be decomposed as the union of two disk bundles must be rationally elliptic. In dimension five, such manifolds are classified up to diffeomorphism, while the same is true in dimension six when either the second Betti number vanishes or the third Betti number is non-trivial.