ETD

Archivio digitale delle tesi discusse presso l'Università di Pisa

Tesi etd-10082018-121502


Tipo di tesi
Tesi di laurea magistrale
Autore
BATTISTA, LUDOVICO
URN
etd-10082018-121502
Titolo
Principal congruence link complements
Dipartimento
MATEMATICA
Corso di studi
MATEMATICA
Relatori
relatore Martelli, Bruno
Parole chiave
  • classification principal congruence manifolds
  • arithmetic manifolds
  • hyperbolic manifolds
Data inizio appello
26/10/2018
Consultabilità
Completa
Riassunto
The aim of the thesis is to define and classify principal congruence manifolds that are diffeomorphic to link complements in S3, the three-dimensional ball.
This is done by presenting results about hyperbolic manifolds with a focus on the arithmetic ones and then following works of Matthias Goerner, Mark D. Baker and Alan W. Reid which were summarized in the recent article “All principal congruence link groups”.
To exclude cases in the classification, principal tools are cuspidal cohomology, which give us algebraic conditions that have to be satisfied in order to let a specific quotient be a link complement, and regular tessellations, that can be proved to be a special case of principal congruence link complements and have a structure that makes them easier to study. The main tool to prove that a specific manifold is a link complement is an algorithm that searches for peripheral curves that can be trivialized to trivialize the whole fundamental group; the fact that this in enough for a manifold to be a link complement is a consequence of Perel’man work.
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