Manifolds and fibre bundles/
Mångfalder och fiberknippen
Number of credits: 7.5 hp
Lecturer: Göran Bergqvist
Course literature: S. Morita, Geometry of Differential Forms (American Mathematical Society).
Supplementary reading: T. Frankel, The Geometry of Physics (Cambridge Univ. Press). I. Madsen and J. Tornehave, From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes (Cambridge Univ. Press). M. Nakahara, Geometry, Topology and Physics (Adam Hilger)
Course contents: Homology and de Rham cohomology. Harmonic forms and Hodge decomposition. Lie groups and Lie algebras. Vector bundles, principal bundles and general fibre bundles; connections, curvature and characteristic classes.
Organisation: Lectures and student seminars.
Examination: Presentations and active participation.
Prerequisites: MAI003 (NMAD11) Differential geometry. Basic knowledge of abstract algebra, topology, and ordinary and partial differential equations.
Last updated: 2022-11-15