Equivariant classification of 2-torus manifolds

Abstract

A 2-torus manifold is a closed smooth manifold of dimension \(n\) with an effective action of a 2-torus group \((\Z_2)^n\) of rank \(n\), and it is said to be locally standard if it is locally isomorphic to a faithful representation of \((\Z_2)^n\) on \(\R^n\). This paper studies the equivariant classification of locally standard 2-torus manifolds.