A compactness theorem in group invariant persistent homology

Quercioli, Nicola (2017) A compactness theorem in group invariant persistent homology. [Laurea magistrale], Università di Bologna, Corso di Studio in Matematica [LM-DM270]
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Abstract

In this thesis we present a new result concerning the theory of group invariant persistent homology. This theory adapts persistent homology in the presence of the action on a space of functions Phi of a subgroup G of the group H of all self-homeomorphisms of a topological space X. Its model is based on a space of suitable operators defined on Phi. After describing the mathematical setting and recalling some basic results, we prove that the space of these operators is compact with respect to a suitable topology. In order to prove this result, we require that Phi, G, X are compact.

Abstract
Tipologia del documento
Tesi di laurea (Laurea magistrale)
Autore della tesi
Quercioli, Nicola
Relatore della tesi
Scuola
Corso di studio
Indirizzo
Curriculum A: Generale e applicativo
Ordinamento Cds
DM270
Parole chiave
group invariant persistent homology group invariant non-expansive operator natural pseudo-distance
Data di discussione della Tesi
31 Marzo 2017
URI

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