On the topology of manifolds with completely integrable geodesic flows II

Abstract

We show that if M is a compact simply connected Riemannian manifold whose geodesic flow is completely integrable with non-degenerate first integrals, then the loop space homology of M grows sub-exponentially. We also show that if for some point p ϵ M, the geodesic flow of M admits action-angle coordinates with singularities in a neighborhood of every vector in the unit sphere at p, then M is Z -elliptic.