Last week got to know the fundamental group of a pointed topological space. We discussed one heuristic example, the fundamental group of the circle. This week we will formally derive that this fundamental group is isomorphic to the additive group of integers. On the way, we will introduce and study covering spaces in some detail.

Learning outcomes

After this week, you should be able to

  • show that the fundamental group of a path-connected space does not depend on the basepoint
  • name important examples of covering spaces (rose with n petals, exponential map, etc)
  • explain Deck transformations and lifts of covers
  • derive the fundamental group of the circle

Tasks and Materials