Differential geometry II - smooth manifolds
Section outline
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Course
- Course book: Fiche de cours
- Lecturer: Dimitri Wyss
- Teaching Assistant: Eric Chen
Time and Place
- Lecture: Thursdays, 08:15 - 10:00, MA A1 10
- Exercise session: Mondays, 15:15 - 17:00, CM 0 12
Notes
We will mostly follow the lecture notes below, but we encourage you to take notes during the lectures for additional information, drawings and intuition.
Literature
- John M. Lee: Introduction to Smooth Manifolds
- Jefrrey M. Lee: Manifolds and Differential Geometry
- Loring W. Tu: An Introduction to Manifolds
- G. Gross, E. Meinrecken: Manifolds, Vector Fields, and Differential Forms - An Introduction to Differential Geometry
Further useful material:
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There will be no exercise session on monday 7th of september. The course starts with an introduction on thursday.
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Due to the holiday on monday 21. there will only be a one hour lecture on thursday, the second hour is transformed into an exercise session for sheet 2.
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Lecture 3:
- The tangent space to a smooth manifold at a point
- The differential of a smooth map
- Computations in local coordinates
Suggestion for self-study: Alternative definitions of the tangent space (pp. 71-73)
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Lecture 4:
- More computations in local coordinates
- Velocity vectors of smooth curves
- The tangent bundle of a smooth manifold
- Definition of smooth immersions, submersions, and embeddings
