Bohr almost periodic maps into 𝐾(𝜋,1) spaces
Sol Schwartzman · Proceedings of the American Mathematical Society · 1997
Let X X be a locally finite simplicial complex of finite topological dimension. Assume further that X X is a K ( π , 1 ) K(\pi ,1) space where π \pi is a group whose only abelian subgroups are infinite cyclic. We prove that a Bohr almost periodic map of the real line into X X is uniformly homotopic to a periodic map. As a consequence we show that a Bohr almost periodic geodesic on a compact Riemannian manifold of everywhere negative curvature is necessarily periodic.