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.
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