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 dim G X = n and H ˇ n ( X ; G ) ≠ 0 , then X is an ( n , G ) -bubble. This implies that any such space X has the following properties: H ˇ n − 1 ( A ; G ) ≠ 0 for every closed separator A of X, and X is an Alexandroff manifold with respect to the class D G n − 2 of all spaces of dimension dim G ≤ n − 2 . We also prove that if X is a homogeneous metric continuum with H ˇ n ( X ; G ) ≠ 0 , then H ˇ n − 1 ( C ; G ) ≠ 0 for any partition C of X such that dim G C ≤ n − 1 . The last provides a partial answer to a question of Kallipoliti and Papasoglu [8].