In this week we will prove the Seifert-van Kampen Theorem and apply it to compute the fundamental group of a whole range of spaces. The focus will be on the geometric ideas that underly the theorem. To better describe and analyse topological spaces, we will introduce the concept of a CW complex, which allows to study spaces systematically by pasting “cells” together using attachment maps.

**Learning outcomes**

After this week, you should be able to

- describe the main ideas in the proof of the Seifert-van Kampen Theorem
- compute the fundamental group of some interesting spaces using this theorem
- describe the fundamental group of real projective space
- construct spaces as CW complexes and characterize their topology

**Tasks and Materials**

- Have a look at the lecture notes when they appear.
- Read pages 5 – 7, 45 – 46 in Hatcher’s book.
- Have a look at the example sheet published this week. The problems should be handed in on Thursday of Week 9

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