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تسجيل مستخدم جديدTopological types of 3-dimensional small covers
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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 $(mathbb{Z}_2)^3$-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 $mathbb{R}P^3$ and $S^1timesmathbb{R}P^2$ with certain $(mathbb{Z}_2)^3$-actions under these six operations. As an application, we classify all 3-dimensional small covers up to $({Bbb Z}_2)^3$-equivariant unoriented cobordism.
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