# name
Cohomologia de varietats i càlcul d’índexs

# metadata.dc.description[].value
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Carles Casacuberta

# metadata.dc.description.abstract[].value
[en] The index calculation that we study is a special case of the Atiyah–Singer theorem, which relates a topological index with an analytical index. By using cohomology in manifolds we state the de Rham theorem, define orientations, and relate the signature of a manifold with characteristic classes by means of a theorem due to Hirzebruch. In the main part of the work, we prove that the signature of a Riemannian manifold is equal to the index of a differential operator closely related with the Hodge Laplacian.

# metadata.dc.rights[].value
cc-by-nc-nd (c) Àngel Picazo Archilla, 2019

# metadata.dc.source[].value
Treballs Finals de Grau (TFG) - Matemàtiques

# metadata.dc.title[].value
Cohomologia de varietats i càlcul d’índexs