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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.

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Last updated: 2022-11-15