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Archivio digitale delle tesi discusse presso l’Università di Pisa

Tesi etd-10112023-192828


Tipo di tesi
Tesi di laurea magistrale
Autore
PISAPIA, IRENE
URN
etd-10112023-192828
Titolo
Hyperbolization Procedures for Cell Complexes
Dipartimento
MATEMATICA
Corso di studi
MATEMATICA
Relatori
relatore Martelli, Bruno
Parole chiave
  • cell complexes
  • hyperbolic manifolds
  • hyperbolization procedures
Data inizio appello
27/10/2023
Consultabilità
Tesi non consultabile
Riassunto
The main subject of the thesis is to investigate on hyperbolization procedures for cell complexes, i.e. on particular functors from some category of cell complexes, to the category of metrized cell complexes. Such a procedure is interesting because it produces complete geodesic metric spaces with bounded curvature, and, in some cases, word hyperbolic groups in the sense of Gromov.
In the first chapter we introduce some basic definitions concerning metric spaces and spaces of curvature bounded from above. In the second chapter we deal with cell complexes, in particular metrized cell complexes. We explain some criteria in order to understand whenever such spaces admit a non-positive or strictly negative curvature. The objects of the third chapter are Coxeter Groups and Coxeter orbifolds, used in the fourth chapter in order to prove weaknesses of some old hyperbolization procedures. In the last two chapters, following the work of Charney and Davis, we present a strict hyperbolization procedure which yelds piecewise hyperbolic cell complexes with strictly negative curvature. This construction concerns particular "manifolds with corners", generated from closed hyperbolic manifolds in arbitrary dimension which involve the arithmetic of quadratic forms.
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