Reflection groups in non-negative curvature

TL;DR

This paper classifies non-negatively curved manifolds with reflection group actions, revealing their structure as classical models or generalized open books, and provides a splitting theorem for their universal covers.

Contribution

It offers an equivariant classification of non-negatively curved manifolds with reflection group actions and describes their fundamental building blocks.

Findings

Manifolds are built from classical constant curvature models or generalized open books.

A splitting theorem for the universal cover of such manifolds is established.

Classification of reflection groups acting on these manifolds is provided.

Abstract

We provide an equivariant description/classification of all complete (compact or not) non-negatively curved manifolds M together with a co-compact action by a reflection group W, and moreover, classify such W. In particular, we show that the building blocks consist of the classical constant curvature models and generalized open books with non negatively curved bundle pages, and derive a corresponding splitting theorem for the universal cover.