Tipus de document
Treball de fi de grauData de publicació
Llicència de publicació
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/185428
The generalised Gauss-Bonnet-Chern theorem as an instance in the theory of characteristic classes
Títol de la revista
Autors
Director/Tutor
ISSN de la revista
Títol del volum
Recurs relacionat
Resum
[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.
Descripció
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Ignasi Mundet i Riera
Matèries (anglès)
Citació
Col·leccions
Citació
MARAVALL LÓPEZ, Javier. The generalised Gauss-Bonnet-Chern theorem as an instance in the theory of characteristic classes. [consulted: 17 of August of 2026]. Available at: https://hdl.handle.net/2445/185428