Differential Geometry I

Description: This is a course on differentiable manifolds based on the first 17 chapters of John Lee's book.

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

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Problem Sets:
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[Problem Set 1] [Solutions]
| Manifolds and maps |

[Problem Set 2] [Solutions]
| Submanifolds, submersions and immersions |

[Problem Set 3] [Solutions]
| Lie groups and vector fields |

[Problem Set 4] [Solutions]
| Vector bundles |

[Problem Set 5] [Solutions]
| Differential forms |

[Problem Set 6] [Solutions]
| Metrics and integration |

[Problem Set 7] [Solutions]
| De Rham cohomology |

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Lecture Notes:
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I. Smooth manifolds
[Chapter 1]

II. Smooth maps
[Chapter 2]

III. Tangent vectors
[Chapter 3]

IV. Submersions, immersions, embeddings
[Chapter 4]

V. Submanifolds
[Chapter 5]

VI. Sard's theorem
[Chapter 6]

VII. Lie groups
[Chapter 7]

VIII. Vector fields
[Chapter 8]

IX. Flows
[Chapter 9]

X. Vector bundles
[Chapter 10]

XI. Cotangent bundle
[Chapter 11]

XII. Tensor product
[Chapter 12]

XIII. Riemannian metrics
[Chapter 13]

XIV. Differential forms
[Chapter 14]

XV. Orientations
[Chapter 15]

XVI. Integration on manifolds
[Chapter 16]

XVII. De Rham cohomology
[Chapter 17]

XVIII. Mayer-Vietoris sequence
[Chapter 17]