Thesis etd-06092017-165309 |
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Thesis type
Tesi di dottorato di ricerca
URN
etd-06092017-165309
Thesis title
Cone-manifolds and hyperbolic surgeries
Academic discipline
MAT/03 - GEOMETRIA
Course of study
MATEMATICA
Supervisors
.
tutor Prof. Martelli, Bruno
commissario Prof.ssa Pardini, Rita
commissario Prof. Porti, Joan
commissario Prof. Francaviglia, Stefano
commissario Prof. Vistoli, Angelo
commissario Prof. Alberti, Giovanni
commissario Prof.ssa Pardini, Rita
commissario Prof. Porti, Joan
commissario Prof. Francaviglia, Stefano
commissario Prof. Vistoli, Angelo
commissario Prof. Alberti, Giovanni
Keywords
- Cone-manifolds
- deformations of hyperbolic structures
- hyperbolic 4-manifolds
- hyperbolic surgeries
Graduation session start date
16/06/2017
Availability
Full
Abstract (Inglese)
Abstract (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).
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).
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