Angle structures on pseudo 3-manifolds

TL;DR

This paper investigates angle structures with area-curvature on triangulated pseudo 3-manifolds, establishing conditions for their existence and implications for hyperbolic 3-manifolds with geodesic boundaries.

Contribution

It provides a necessary and sufficient condition for the existence of angle structures with area-curvature on pseudo 3-manifolds, linking geometric structures to topology.

Findings

Existence of angle structures implies hyperbolic 3-manifolds with geodesic boundary admit such structures.

Derived topological information from the existence of angle structures.

Established a criterion for angle structures with area-curvature on pseudo 3-manifolds.

Abstract

It is still not known whether a hyperbolic 3-manifold admits an angle structure or not. We consider angle structures with area-curvature on triangulated pseudo 3-manifolds M in this article. A suficient and necessary condition for the existence of such angle structures is established. As a consequence, any compact hyperbolic 3-manifold with totally geodesic boundary admits an angle structure. We also derive certain topological information of M from the existence of such angle structures.