A Primer on Smooth Manifolds

Contents
Preface
About the Author
1. Charts, Atlases, and Smooth Manifolds
	1.1 Charts and Atlases
	1.2 Topological Spaces
	1.3 Smooth Manifolds
2. Smooth Maps and Submanifolds
	2.1 Smooth Functions
	2.2 Smooth Maps
	2.3 Submanifolds
3. Tangent Vectors
	3.1 Tangent Spaces
	3.2 Tangent Maps
	3.3 The Tangent Bundle
4. Full Rank Smooth Maps
	4.1 Full Rank Maps
	4.2 Rank Theorem
	4.3 Embeddings
5. Vector Fields
	5.1 Vector Fields: An Algebraic Definition
	5.2 Vector Fields and Fields of Vectors
	5.3 Vector Fields and Smooth Maps
6. Flows and Symmetries
	6.1 Integral Curves of a Vector Field
	6.2 Flow of a Vector Field
	6.3 Symmetries and Infinitesimal Symmetries
7. Covectors and Differential 1-Forms
	7.1 Covectors and the Cotangent Bundle
	7.2 Differential 1-Forms and Fields of Covectors
	7.3 Differential 1-Forms and Smooth Maps
8. Differential Forms and Cartan Calculus
	8.1 Algebraic Preliminaries: Alternating Forms
	8.2 Higher-Degree Differential Forms
	8.3 Cartan Calculus
9. Vector Bundles
	9.1 Vector Bundles and Vector Bundle Maps
	9.2 Sections and Frames
	9.3 Constructions with Vector Bundles
10. Integration on Manifolds
	10.1 Oriented Manifolds
	10.2 Integral of a Differential Form
	10.3 Stokes Theorem
Bibliography
Index