In this paper we study the (equivariant) topological types of a class of 3-dimensional closed manifolds (i.e., 3-dimensional small covers), each of which admits a locally standard (ℤ2)3-action such that its orbit space is a simple convex 3-polytope. We introduce six equivariant operations on 3-dimensional small covers. These six operations are interesting because of their combinatorial natures. Then we show that each 3-dimensional small cover can be obtained from ℝ P3 and S1 × ℝ P2 with certain (ℤ2)3-actions under these six operations. As an application, we classify all 3-dimensional small covers up to (ℤ2)3-equivariant unoriented cobordism.
© de Gruyter 2011