Homogeneous ANR-spaces and Alexandroff manifolds

We specify a result of Yokoi [18] by proving that if G is an abelian group and X is a homogeneous metric ANR   compactum with dimGX=n and Hˇn(X;G)≠0, then X   is an (n,G)(n,G)-bubble. This implies that any such space X   has the following properties: Hˇn−1(A;G)≠0 for every closed separator A of X, and X   is an Alexandroff manifold with respect to the class DGn−2 of all spaces of dimension dimG≤n−2dimG≤n−2. We also prove that if X   is a homogeneous metric continuum with Hˇn(X;G)≠0, then Hˇn−1(C;G)≠0 for any partition C of X   such that dimGC≤n−1. The last provides a partial answer to a question of Kallipoliti and Papasoglu [8].