6-dimensional manifolds with effective T4-actions

Abstract Suppose the four dimensional torus T 4 acts effectively on a 6-manifold M so that the orbit space M ∗ is a closed 2-disk, and there exist no exceptional orbits, and the isotropy groups span T 4 . Then the fundamental group of M is a finite abelian group with at most two generators. In this paper, we obtain a homology classification of manifolds of this type under an additional hypothesis that one of the two generators is trivial. We then use this result to obtain a complete classification of simply connected 6-manifolds supporting effective T 4 -actions.