Torus manifolds and non-negative curvature

Wiemeler, Michael

Abstract

A torus manifold M  is a 2n-dimensional orientable manifold with an effective action of an -dimensional torus such that M^T\neq\emptyset. In this paper, we discuss the classification of torus manifolds which admit an invariant metric of non-negative curvature. If M is a simply connected torus manifold which admits such a metric, then M  is diffeomorphic to a quotient of a free linear torus action on a product of spheres. We also classify rationally elliptic torus manifolds with up to homeomorphism.