Class Notes Algebraic Topology of Smooth Manifolds
(SS 2026)
Disclaimer: As this is a newly developed class, this is the first version of these notes. Please do expect some errors and inconsistencies.
- Complete notes (154 pages, last updated July 24, 2026)
- Chapter 0: Introduction
- Chapter 1: Simplicial Complexes
- Chapter 2: The Construction of Simplicial Homology
- Chapter 3: Chain Homotopies
- Chapter 4: The Mayer-Vietoris Sequence in Simplicial Homology
- Chapter 5: Simplicial Cohomology
- Chapter 6: The Construction of Singular Homology
- Chapter 7: The Mayer-Vietoris Sequence in Singular Homology
- Chapter 8: Comparison of Simplicial and Singular Homology
- Chapter 9: Applications of Homology
- Chapter 10: Manifolds
- Chapter 11: Submanifolds
- Chapter 12: Vector Bundles
- Chapter 13: Differential Forms and De Rham Cohomology
- Chapter 14: Integration of Differential Forms
- Chapter 15: Comparison of Singular and De Rham Cohomology
- Chapter 16: Poincaré Duality
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