Point leaf maximal singular Riemannian foliations in positive curvature (Q2274354)

The author introduces the notion of a point leaf maximal singular Riemannian foliation, which can be thought of as a generalization of a fixed point homogeneous isometric group action. The main result of the paper is a classification of such manifolds which are closed, connected, and have positive curvature. Namely, if the manifold is simply connected, then it either is homeomorphic to a sphere or has the cohomology ring of a CROSS. If it is not simply connected, then it is either homeomorphic to a spherical space form or a \(\mathbb{Z}_2\)-quotient of an odd-dimensional cohomology complex projective space.