On the constructions of free and locally standard $\mathbb{Z}_{2}$-torus actions on manifolds

Abstract

We introduce an elementary way of constructing principal $(\mathbb{Z}_{2})^{m}$-bundles over compact smooth manifolds. In addition, we will define a general notion of locally standard $(\mathbb{Z}_{2})^{m}$-actions on closed manifolds for all $m \geq 1$, and then give a general way to construct all such $(\mathbb{Z}_{2})^{m}$-actions from the orbit space. Some related topology problems are also studied.