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Topological types of 3-dimensional small covers

By Zhi Lü and Li Yu

Abstract

Abstract. 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 RP 3 and S 1 × RP 2 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. 1

Year: 2012
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