A Topological Splitting Theorem for Poincare Duality Groups and High-dimensional Manifolds

We show that for a wide class of manifold pairs N, M satisfying dim(M) = dim(N) + 1, every pi_1-injective map f : N --> M factorises up to homotopy as a finite cover of an embedding. This result, in the spirit of Waldhausens torus theorem, is derived using Cappells surgery methods from a new algebraic splitting theorem for Poincare duality groups. As an application we derive a new obstruction to the existence of pi_1-injective maps.