Equivariant classification of 2-torus manifolds

TL;DR

This paper classifies locally standard 2-torus manifolds, which are smooth manifolds with effective $( ext{Z}_2)^n$ actions, providing a systematic understanding of their equivariant structures.

Contribution

It introduces a classification framework for locally standard 2-torus manifolds based on their equivariant properties, advancing the understanding of their topological and group action structures.

Findings

Provides a classification scheme for locally standard 2-torus manifolds

Establishes invariants for equivariant classification

Enhances understanding of $( ext{Z}_2)^n$ actions on 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.