Sumários
Principal bundles
18 dezembro 2018, 11:00 • Sílvia Nogueira da Rocha Ravasco dos Anjos
The notion of fibre bundle with group structure G. Morphism of fibre bundles with group structure G.
Characteristic classes (cont.)
17 dezembro 2018, 11:00 • Sílvia Nogueira da Rocha Ravasco dos Anjos
The Chern-Weil homomorphism. Pontryagin classes.
Characteristic classes.
11 dezembro 2018, 11:00 • Sílvia Nogueira da Rocha Ravasco dos Anjos
Differential forms in M with values in the total space E of a vector bundle over M. De Rham cohomology of M with coefficients in the total space E of a vector bundle over M.
Curvature and holonomy
10 dezembro 2018, 11:00 • Sílvia Nogueira da Rocha Ravasco dos Anjos
Curvature tensor and curvature 2-form. Structure equations. Bianchi's identity. Holonomy of a connection. Holonomy representation of a flat connection.
Connections
4 dezembro 2018, 11:00 • Sílvia Nogueira da Rocha Ravasco dos Anjos
The notion of connection in a vector bundle. Definition of Christoffel symbols and 1-forms of the connection. The covariant derivative of a section and parallel transport along a smooth path.