Cone-manifolds and hyperbolic surgeries

We first introduce hyperbolic, Euclidean, and spherical cone-manifolds of arbitrary dimension. After that, we carefully describe a deforming hyperbolic 4-polytope of finite volume. Finally, we glue copies of that polytope to get some interesting deformations of hyperbolic cone-manifolds of dimension four. In particular, we discover some four-dimensional instances of Thurston's hyperbolic Dehn surgery and degeneration. We also find the smallest known hyperbolic 4-manifold that is not commensurable with the integral lattice of O(4,1).