Thick triangulations of hyperbolic n-manifolds

TL;DR

This paper proves that complete hyperbolic n-manifolds can be triangulated with thick parts closely resembling Euclidean simplices, with bounds depending only on dimension and the thick-thin decomposition constant.

Contribution

It establishes the existence of controlled geodesic triangulations of hyperbolic n-manifolds with thick parts bilipschitz equivalent to Euclidean simplices, depending only on dimension and decomposition parameters.

Findings

Thick parts of hyperbolic n-manifolds admit bilipschitz triangulations.

The bilipschitz constant depends only on dimension and the thick-thin constant.

Triangulations facilitate geometric and topological analysis of hyperbolic manifolds.

Abstract

We show that a complete hyperbolic n-manifold has a geodesic triangulation such that the tetrahedra contained in the thick part are L-bilipschitz diffeomorphic to the standard Euclidean n-simplex, for some constant L depending only on the dimension and the constant used to define the thick-thin decomposition of M.