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

TL;DR

The paper introduces a new elementary method for constructing principal (Z_2)^m-bundles over compact manifolds and provides a general framework for locally standard (Z_2)^m-actions, linking them to their orbit spaces.

Contribution

It offers a novel elementary construction approach for principal (Z_2)^m-bundles and a comprehensive method to generate all locally standard (Z_2)^m-actions from orbit spaces.

Findings

New elementary construction method for principal (Z_2)^m-bundles

General framework for locally standard (Z_2)^m-actions

Connections between actions and their orbit spaces

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.