Angle structures 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.