Operations on 3-dimensional small covers

Abstract

The purpose of this paper is to study relations among equivariant operations on 3-dimensional small covers. The author gets three formulas for these operations. As an application, the Nishimura’s theorem on the construction of oriented 3-dimensional small covers and the Lü-Yu’s theorem on the construction of all 3-dimensional small covers are improved. Moreover, for a construction of 3-dimensional 2-torus manifolds, it is shown that all operations can be obtained by using the equivariant surgeries.

Keywords

Equivariant surgery / Finite group action / Small cover / 3-dimensional manifold / 3-dimensional simple polytope

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