The geometry of branched coverings of hyperbolic manifolds

TL;DR

This paper explores the geometric characteristics of branched covers of closed hyperbolic manifolds along totally geodesic submanifolds, providing a comprehensive overview of known results in a clear form.

Contribution

It compiles and clarifies existing geometric properties of branched covers of hyperbolic manifolds, making them more accessible to researchers.

Findings

Discusses geometric properties of branched covers in hyperbolic manifolds.

Provides a clear presentation of results known to experts but hard to find.

Focuses on covers branched along totally geodesic submanifolds.

Abstract

We discuss geometric properties of covers of closed hyperbolic manifolds of dimension $n\geq 3$, branched along a totally geodesic codimension two submanifold $\Sigma$. The results are mostly known to the experts but hard to find in the literature in this form.