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Tesi etd-07262021-203400


Tipo di tesi
Tesi di dottorato di ricerca
Autore
CALDEIRA PIRES FERRARI, LEONARDO HENRIQUE
URN
etd-07262021-203400
Titolo
Hyperbolic Manifolds and Coloured Polytopes
Settore scientifico disciplinare
MAT/03
Corso di studi
MATEMATICA
Relatori
tutor Prof. Martelli, Bruno
Parole chiave
  • hyperbolic geometry
  • manifold cover
  • polytopes
  • real toric manifolds
  • sagemath
Data inizio appello
29/07/2021
Consultabilità
Completa
Riassunto
In this thesis, we explore the possibilities of Davis-Januszkiewicz (1991) techniques to build manifold covers of right-angled polytopes. Combining these techniques with Choi-Park (2017) work on the cohomology ring of real toric manifolds, and with computational algorithms in Sagemath, we classify up to isometry all possible cusp sections of finite-volume, orientable, hyperbolic 4-manifolds obtained as manifold covers of right-angled polytopes. We also obtain the first example of an orientable, cusped hyperbolic 4-manifold such that all cusp sections are rational homology spheres. This answers in particular to an open question from Golénia-Moroianu (2012) and provides a counter-example to Mazzeo-Phillips (1990).
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