讲义: Differentiable Manifolds

原作者: Dieter Kotschick

本讲义是 2023-2024 年 Ludwig-Maximilians-Universität 冬季学期微分流形讲义.

讲义 PDF 链接: https://xumin-liang.net/c/files/differentiable_manifolds.pdf

讲义对应练习题 PDF 链接: https://xumin-liang.net/c/files/Differentiable_Manifolds_Problem_Sheets.pdf

目录

	1 Topology
	2 Differentiable Manifold
	3 Tangent Spaces and Tangent Bundle
	4 Paracompactness
	5 Submanifold
	6 Smooth Vector Bundles
	7 Flows
	8 Lie Theory
	9 The Frobenius Theorem
	10 Differential Forms and Multilinear Algebra
	11 Integration of Forms
	12 de Rham Cohomology
	13 Connections and Curvature
	14 The Euler Class