Topics for the exam

The following is a list of the most central themes that are relevant for discussion during the oral exam.

- Smooth manifolds

- Smooth maps

- Partitions of unity

- Tangent spaces and differentials

- Submanifolds

- Quotient spaces

- Immersions and submersions

 

- Tangent bundles

- Vector fields and Lie brackets

- Flows of vector fields

- Lie groups

 

- Co-tangent spaces/bundles and differential 1-forms

- Tensors and alternating tensors

- Wedge product and exterior algebra

- Differential forms

- Exterior derivative

- Orientations

- Integration on manifolds

- Stoke’s theorem

- de Rham cohomology

- Mayer-Vietoris sequence

- Homotopy invariance 

Published May 11, 2024 2:23 PM - Last modified May 14, 2024 12:53 PM