Angle structure on general hyperbolic 3-manifolds

TL;DR

This paper proves that certain non-compact hyperbolic 3-manifolds with geodesic boundary can be subdivided into ideal tetrahedra with angle structures, enhancing understanding of their geometric decompositions.

Contribution

It establishes the existence of ideal triangulations with angle structures for a class of hyperbolic 3-manifolds under specific topological conditions.

Findings

Existence of ideal triangulations with angle structures for these manifolds

Subdivision of mixed ideal polyhedral decompositions

Application of topological conditions to ensure triangulation properties

Abstract

Let $M$ be a non-compact hyperbolic $3$-manifold with finite volume and totally geodesic boundary components. By subdividing mixed ideal polyhedral decompositions of $M$, under some certain topological conditions, we prove that $M$ has an ideal triangulation which admits an angle structure.