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