Differential Geometry I

Description: These are lecture notes based on the first 17 chapters of John Lee's book.

Reference:
J.M. Lee, Introduction to Smooth Manifolds

Problem sheets:
Problem Sheet 1
Problem Sheet 2
Problem Sheet 3

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Lecture Notes:
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[Chapter 1] Smooth manifolds

[Chapter 2] Smooth maps

[Chapter 3] Tangent vectors

[Chapter 4] Submersions, immersions, embeddings

[Chapter 5] Submanifolds

[Chapter 6] Sard's theorem

[Chapter 7] Lie groups

[Chapter 8] Vector fields

[Chapter 9] Flows

[Chapter 10] Vector bundles

[Chapter 11] Cotangent bundle

[Chapter 12] Tensor product

[Chapter 13] Riemannian metrics

[Chapter 14] Differential forms

[Chapter 15] Orientations

[Chapter 16] Integration on manifolds

[Chapter 17] De Rham cohomology