Document type
Master thesisPublication date
Publication license
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/216890
Topological approaches to Euler characteristics in odd-dimensional orbifolds
Journal Title
Authors
Director/Tutor
Journal ISSN
Volume Title
Related resource
Abstract
This master thesis deals with orbifolds, a generalization of manifolds.
On one hand, for compact manifolds of odd dimension one has a pretty interesting formula: the Euler characteristic of the manifold is half the characteristic of its boundary. On the other hand, Ichiro Satake stated and proved in 1957 that the Euler characteristic of an odd-dimensional compact Riemannian orbifold without boundary is 0.
From this last result it can be proven a generalisation of the formula for odd-dimensional compact smooth orbifolds. Nevertheless, the proof given by Satake uses the Chern-Gauss-Bonnet formula, so the objective of this Master Thesis is to give a purely topological proof of the formula described.
For this, the idea is to dissect an orbifold into smaller parts where the study of this formula becomes easier. In the following we define the main characteristics and properties of orbifolds, as well as some of their topological and geometrical features.
Description
Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2023-2024. Director: Joan Porti i Ignasi Mundet i Riera
Subject (English)
Citation
Collections
Citation
GALLARDO CAMPOS, Ramon. Topological approaches to Euler characteristics in odd-dimensional orbifolds. [consulted: 14 of June of 2026]. Available at: https://hdl.handle.net/2445/216890