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

We investigate what kind of closed 3-manifolds can admit locally standard (Z(2))(3)-actions. In particular, we will prove that for a closed connected 3-manifold M with H-1 (M; Z(2)) = 0, M admits a locally standard (Z(2))(3)-action if and only if M is a connected sum of 8 copies of a Z(2)-homology sphere N. So if such an M is irreducible, it must be homeomorphic to S-3. Moreover, the argument can be extended to study orientable rational homology 3-spheres M with H-1 (M; Z(2)) congruent to Z(2) which admits locally standard (Z(2))(3)-actions. (C) 2013 Elsevier B.V. All rights reserved.