We prove the following result announced by the second and third authors: Any homogeneous, metric $ANR$-continuum is a $V_{G}^{n}$-continuum provided ${{\dim}_{G}}X\,=\,n\,\ge \,1$ and ${{\overset{\vee }{\mathop{H}}\,}^{n}}\left( X;\,G \right)\,\ne \,0$, 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 ${{\overset{\vee }{\mathop{H}}\,}^{n}}\left( X;\,G \right)\,\ne \,0$ for some group $G$ and $n\,\ge \,1$, cannot be separated by a compactum $K$ with ${{\overset{\vee }{\mathop{H}}\,}^{n-1}}\left( K;\,G \right)\,=\,0$ and ${{\dim}_{G}}K\,\le \,n\,-\,1$. 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.