Tipo di tesi
Tesi di dottorato di ricerca
Titolo
Cone-manifolds and hyperbolic surgeries
Settore scientifico disciplinare
MAT/03 - GEOMETRIA
Corso di studi
MATEMATICA
Parole chiave
- Cone-manifolds
- deformations of hyperbolic structures
- hyperbolic 4-manifolds
- hyperbolic surgeries
Data inizio appello
16/06/2017
Riassunto (Italiano)
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).
