After successful completion of the course, students are able to...

• ... recall and motivate the definition of topological and smooth manifolds and to prove some elementary properties of these structures.
• ... define (co-)tangential spaces and (co-)vector fields and to relate these concepts with the differentiation of functions, respectively with differential forms, on smooth manifolds.
• ... distinguish between submersions and immersions and to decide, when an submanifold is called embedded.
• ... define the Lie bracket of vector fields and to explain how the tangentialspace of a smooth manifold is turned into an Lie algebra.
• ... explain how the left cosets of a Lie group with respect to a closed Lie subgroup carry the structure of a homogeneous space.
• ... explain the product of differential forms and the (outer) derivative.
• ... explain how to integrate a differentialform over a manifold and to formulate and prove Stokes' Theorem on smooth manifolds.

Exercise classes for the corresponding course

Exercise will be posted at least a week before class. During class students will present their solutions to the exercises.

The exercise course will be held via TUWEL.

There will be Problemsheets posted on TUWEL and grading will be done based on your Solutions to these Problems. See TUWEL for further informations.