On the constructions of free and locally standard Z_2-torus actions on Manifolds

Abstract

We introduce an elementary way of constructing principal (Z_2)^m-bundles over compact smooth manifolds. In addition, we will define a general notion of locally standard (Z_2)^m-actions on closed manifolds for all m>0, and then give a general way to construct all such (Z_2)^m-actions from the orbit space. Some related topology problems are also studied.

28 pages, 12 figures, some minor revisions are made, one picture and one reference are added.