Differential geometry II - smooth manifolds
Weekly outline
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Course
- Course book: Fiche de cours
- Lecturer: Nikolaos Tsakanikas (nikolaos.tsakanikas@epfl.ch)
- Teaching Assistant: Linus Erik Rösler (linus.rosler@epfl.ch)
Time and Place
- Lecture: Mondays, 17:15 - 19:00, MA A3 31
- Exercise session: Thursdays, 16:00 - 17:30, INM 200
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
Material from previous versions of the course:
- Lecture notes by Marcos Cossarini (2021)
- Videos by Yash Lodha (2020)
Further useful material:
Assessment Methods
- Exercises: There will be an exercise sheet every week, which will be discussed thoroughly in the exercise sessions. The solution to one designated exercise from each weakly exercise sheet must be submitted the following week (Thursdays). The submissions will be corrected and graded. They will account for 25% of the final grade.
- Exam: There will be a written exam, which will account for 75% of the final grade.
- Course book: Fiche de cours
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Lecture 1:
- Introduction to the course
- Definition and examples of topological manifolds
- Definition of smooth manifolds
Literature: John M. Lee, Introduction to Smooth Manifolds, Chapter 1
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Lecture 2:
- Examples of smooth manifolds
- Definition and basic properties of smooth maps
- Diffeomorphisms
Literature: John M. Lee, Introduction to Smooth Manifolds, Chapter 1 and Chapter 2
Schedule change: Since Monday the 16th of September is a public holiday, the 2nd Lecture will take place instead on Wednesday the 18th of September from 16:15 to 18:00 in GC A3 31, see here. -
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Lecture 4:
- The tangent space to a smooth manifold at a point
- The differential of a smooth map
- Computations in local coordinates
Literature: John M. Lee, Introduction to Smooth Manifolds, Chapter 3
- The tangent space to a smooth manifold at a point
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Lecture 6:
- The Rank theorem
- Applications of the Rank theorem
Literature: John M. Lee, Introduction to Smooth Manifolds, Chapter 4 -
Autumn holidays: No lecture and no tutorial will take place this week!
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