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Archivio digitale delle tesi discusse presso l’Università di Pisa

Tesi etd-09032022-001357


Tipo di tesi
Tesi di laurea magistrale
Autore
ULLIANA, ANDREA
URN
etd-09032022-001357
Titolo
Distribuzioni non integrabili e il Complesso di Rumin
Dipartimento
MATEMATICA
Corso di studi
MATEMATICA
Relatori
relatore Prof. Alberti, Giovanni
Parole chiave
  • characteristic set
  • contact manifold
  • Heisenberg group
  • rectifiable set
  • Riemmanian approximation.
  • Rumin complex
Data inizio appello
23/09/2022
Consultabilità
Completa
Riassunto
Rumin complex is a complex of differential forms adapted to a contact geometry. It is defined from De Rham's one by a fairly complicated algebraic procedure. Despite having many good properties, Rumin complex does not emerge so naturally from the current literature.

Our goal is to define Rumin Complex in a natural way. This is not fully realized, but satisfactory partial results are obtained. The approach is the following: we approximate the Heisenberg Group with Riemannian manifolds, in order to consider the limit of De Rham complexes of the approximating manifolds. The resulting limit is a complex of forms strictly related to Rumin's one.

We also discuss the dual problem: the notion of regular surface and rectifiable set within Heisenberg group. One of the main result we present is that every rectifiable subset of high dimension of Heisenberg group is trivial. We also highlight a connection between this theorem and the theory of Characteristic Sets.
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