Reflection groups in non-negative curvature

Abstract

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