Document type
Bachelor thesisPublication date
Publication license
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/68870
Nombres $p$-àdics i aplicacions en física i topologia
Journal Title
Authors
Director/Tutor
Additional contribution
Journal ISSN
Volume Title
Abstract
In this undergraduate thesis we begin by introducing the $p$-adic numbers and their basic properties, as well as the adeles. We then give an application to particle physics, using adeles extensively, to regularize divergent products through a product formula thereby endowing them of precise meaning. Next we discuss the topological differences between p-adic numbers and real numbers, and show some kind of euclidean models for them. This will prove helpful in the last chapter, where we will prove an equivalence of topological conjectures, which has been one of the goals of the project. Finally, we give a general approach to how the proof by Pardon [17] of the 3-dimensional case of this conjecture, which uses this equivalence, is carried out.
Description
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2015, Director: Artur Travesa i Grau
Related resource
Subject (English)
Citation
Collections
Citation
FERRÉ MORAGUES, Andreu. Nombres $p$-àdics i aplicacions en física i topologia. [consulted: 5 of October of 2026]. Available at: https://hdl.handle.net/2445/68870