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Title: The generalised Gauss-Bonnet-Chern theorem as an instance in the theory of characteristic classes
Author: Maravall López, Javier
Director/Tutor: Mundet i Riera, Ignasi
Keywords: Formes diferencials
Treballs de fi de grau
Geometria diferencial
Varietats diferenciables
Differential forms
Bachelor's theses
Differential geometry
Differentiable manifolds
Issue Date: 20-Jun-2021
Abstract: [en] The Gauss-Bonnet theorem is one of the earliest classical results in differential geometry. It provides a link between the topology and the geometry of a smooth surface (that is, a smooth 2-manifold). A well-known, highly non-trivial generalisation of this to arbitrary (finite) dimension exists, which was first proven intrinsically (in other words, without recourse to the existence of an embedding of the manifold into an Euclidean space) by Shiing-Shen Chern in 1944. The aim of this work is to provide a full proof of a slightly more general result, which is valid for arbitrary vector bundles over a differential manifold, that gives as a direct corollary the Gauss-Bonnet-Chern theorem when considering the tangent bundle.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Ignasi Mundet i Riera
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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