MAS61015 Algebraic Topology
Contents
- 1 Introduction
- 2 The idea of homology
- 3 Topological spaces
- 4 Homeomorphism
- 5 Paths
- 6 Interlude on categories and functors
- 7 Constructing new spaces
- 8 The Hausdorff property, and compactness
- 9 Homotopy
- 10 Homology
- 11 Homology of the punctured plane
- 12 Abelian groups
- 13 Chain complexes and homology
- 14 Chain homotopy
- 15 Homology of spheres
- 16 Applications of homology
- 17 The Snake Lemma
- 18 Subdivision
- 19 Construction of the Mayer-Vietoris sequence
- 20 Further calculations
- 21 The Jordan Curve Theorem
- 22 Covering maps
- 23 Transfers, coefficients and homology of projective spaces
- 24 Borsuk-Ulam and related results