Orbifolds from a metric viewpoint

TL;DR

This paper characterizes Riemannian orbifolds and their coverings using metric geometry, revealing how certain metric doubles form new orbifolds and how projections serve as orbifold coverings.

Contribution

It introduces a metric-based characterization of Riemannian orbifolds and their coverings, including the construction of metric doubles along specific strata.

Findings

The metric double of a Riemannian orbifold along the closure of its codimension one stratum is itself a Riemannian orbifold.

The natural projection from the metric double to the original orbifold is an orbifold covering.

Provides a metric geometric perspective on orbifold structures and coverings.

Abstract

We characterize Riemannian orbifolds and their coverings in terms of metric geometry. In particular, we show that the metric double of a Riemannian orbifold along the closure of its codimension one stratum is a Riemannian orbifold and that the natural projection is an orbifold covering.