Complete Hyperbolic Structure on Manifold

Abstract

In this thesis we have studied the way to determine if the hyperbolic structure on 3- manifold is complete. These tools can be to used to find complete hyperbolic structure on 3-manifolds using ideal triangulation. We will look at how to decompose the 8-knot complement. The algorithm thus developed can be applied to find ideal triangulation of knot. We study the relation between developing maps and completeness of the (G,X) structure on a manifold