On 3-manifolds with locally standard (Z2)3-actions

We investigate what kind of closed 3-manifolds can admit locally standard (Z2)3-actions. In particular, we will prove that for a closed connected 3-manifold M with H1(M;Z2)=0, M admits a locally standard (Z2)3-action if and only if M is a connected sum of 8 copies of a Z2-homology sphere N. So if such an M is irreducible, it must be homeomorphic to S3. Moreover, the argument can be extended to study orientable rational homology 3-spheres M with H1(M;Z2)≅Z2 which admits locally standard (Z2)3-actions.