The geometry of branched coverings of hyperbolic manifolds

Abstract

We discuss geometric properties of covers of closed hyperbolic manifolds of dimension $n\ge 3$, 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.

17 pages. The article was written in the style of a survey as a final report for the DFG priority program "Geometry at infinity", licensed by Springer Publ. Comp