# Part II - Algebraic Topology

## Lectured by H. Wilton, Michaelmas 2015

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# Contents

- V Full version
- 0 Introduction
- 1 Definitions
- 2 Homotopy and the fundamental group
- 3 Covering spaces
- 3.1 Covering space
- 3.2 The fundamental group of the circle and its applications
- 3.3 Universal covers
- 3.4 The Galois correspondence
- 4 Some group theory
- 4.1 Free groups and presentations
- 4.2 Another view of free groups
- 4.3 Free products with amalgamation
- 5 Seifert-van Kampen theorem
- 5.1 Seifert-van Kampen theorem
- 5.2 The effect on pi1 of attaching cells
- 5.3 A refinement of the Seifert-van Kampen theorem
- 5.4 The fundamental group of all surfaces
- 6 Simplicial complexes
- 7 Simplicial homology