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

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

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