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Tesi etd-06092017-165309


Tipo di tesi
Tesi di dottorato di ricerca
Autore
RIOLO, STEFANO
URN
etd-06092017-165309
Titolo
Cone-manifolds and hyperbolic surgeries
Settore scientifico disciplinare
MAT/03
Corso di studi
MATEMATICA
Commissione
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
Parole chiave
  • hyperbolic 4-manifolds
  • deformations of hyperbolic structures
  • hyperbolic surgeries
  • Cone-manifolds
Data inizio appello
16/06/2017;
Disponibilità
completa
Riassunto analitico
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).
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