Alexandroff Manifolds and Homogeneous Continua

We prove the following result announced by the second and third authors: Any homogeneous, metric ANR-continuum is a V-G(n)-continuum provided dim(G) X = n >= 1 and H-n(X;G) not equal 0, where G is a principal ideal domain. This implies that any homogeneous n-dimensional metric ANR-continuum is a V-n-continuum in the sense of Alexandroff. We also prove that any finite-dimensional cyclic in dimension n homogeneous metric continuum X, satisfying H-n(X;G) not equal 0 for some group G and n >= 1, cannot be separated by a compactum K wit Hn-1 (K; G) = 0 and dim(G) K <= n - 1. This provides a partial answer to a question of Kallipoliti-Papasoglu as to whether a two-dimensional homogeneous Peano continuum can be separated by arcs.