A dense G-delta set of Riemannian metrics without the finite blocking property

Abstract

A pair of points (x,y) in a Riemannian manifold (M,g) is said to have the finite blocking property if there is a finite set P contained in M\{x,y} such that every geodesic segment from x to y passes through a point of P. We show that for every closed C-infinity manifold M of dimension at least two and every pair (x,y) in M x M, there exists a dense G-delta set of C-infinity Riemannian metrics on M such that (x,y) fails to have the finite blocking property for every g in that set.