Polopoly will be shut down December 15, 2023. Existing pages will have to be moved before or will be removed at that date. Empolyees may read more at FAQ Polopoly Avveckling

MAI0038
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.

Page manager: karin.johansson@liu.se
Last updated: 2022-11-15