%0 Journal Article %T A Topological Splitting Theorem for Poincare Duality Groups and High-dimensional Manifolds %A Aditi Kar %A Graham A. Niblo %J Mathematics %D 2011 %I arXiv %X 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 Waldhausen's torus theorem, is derived using Cappell's 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. %U http://arxiv.org/abs/1110.2041v3