Jeffrey Lee, Jeffrey Marc Lee. Chapter. 1. Differentiable. Manifolds. – Hermann Weyl In this chapter we introduce differentiable manifolds and smooth maps. Buy Foundations of Differentiable Manifolds and Lie Groups (Graduate Texts in Mathematics) on ✓ FREE SHIPPING on qualified orders. The official textbook for the course is John Lee, Introduction to smooth manifolds, free through Columbia's library. We will also use Guillemin & Pollack.


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There is also a section that derives the exterior calculus version of Maxwell's equations. The first chapters of the book are suitable for a one-semester course on manifolds. There is more lee differentiable manifolds enough material for a year-long course on manifolds and geometry.

Vector fields and flows.

Math 214: Differentiable manifolds

Lie derivatives and Lie brackets. Distributions and Frobenius' Theorem.

Lie groups and Lie algebras. Differential forms and Tensor fields. Differential and Cartan Calculus.


Integration on manifolds and Stokes Formula. You can find my lecture notes herebut the following two textbooks lee differentiable manifolds highly recommended. See the contents and first chapter here.

Grading Policy and Exams There will be weekly homework, 1 midterm and a final exam. Homework problems are to be assigned once a week.

Math 518 - Differentiable Manifolds I - Fall 2013

They are due the following week, at the beginning lee differentiable manifolds the Friday class. No late homework will be accepted. The two worst homework grades will be dropped.


On Fridays, one homework problem will be discussed in class, with the participation of the students and this will be taken into account for the grade. The midterm will take place on Friday, October 11, in the regular classroom the date lee differentiable manifolds subject to change.

Lee, chapters 4 and 5 Transversality and Sard's theorem.

Math - Differentiable Manifolds I - Fall

For more about this see Guillemin and Pollack. Vector fields and Lie bracket. Lee, chapter 8 Lie groups and Lie algebras. Lee, chapters 7 and 8 Flows and the Lie derivative. Lee, chapter 9 Vector bundles, tensors. Lee, chapters 10, 11, lee differentiable manifolds Riemannian metrics.

Reference request - Introductory texts on manifolds - Mathematics Stack Exchange

Lee, chapter 13 Differential forms and Stokes' theorem. Lee, chapters lee differentiable manifolds, 15, For alternate treatments see Guilleman and Pollack or Bott and Tu. Lee, chapters 17, 18 Distributions and foliations. Lee, chapter 19 A bit of Morse theory if time permits; not covered in Lee's book.

Homework The course grade will be based on homework, which will be due at the beginnig of class on Tuesdays. There might be no homework on occasional weeks if we have not covered lee differentiable manifolds material for a new assignment.

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