Almost Isotropy-Maximal Manifolds of Non-negative Curvature

Abstract

We extend the equivariant classification results of Escher and Searle for closed, simply connected, non-negatively curved Riemannian $n$-manifolds admitting isometric isotropy-maximal torus actions to the class of such manifolds admitting isometric strictly almost isotropy-maximal torus actions. In particular, we prove that such manifolds are equivariantly diffeomorphic to the free, linear quotient by a torus of a product of spheres of dimensions greater than or equal to three.

Section 3 rewritten to streamline arguments. Remark 1.1 from previous version is now Theorem B. To appear in Transactions of the AMS