Small Deformations of a complete 3-dimensional Hyperbolic structure

In this talk, I will first introduce the notion of complete hyperbolic structure. I will then discuss how one can a construct complete hyperbolic manifold by gluing faces of polyhedra. Then I will explain what we mean by small deformations and how one can capture useful information about them using the notion of cusp parameters (discussed in [1]). 

[1]: Walter D. Neumann and Don Zagier. “Volumes of hyperbolic three-manifolds.” Topology 24 (1985), no. 3, 307-332.