In Week 2 we will introduce Homotopy, which allows to study continuous deformations of spaces. We will see what it means for a space to be contractible. We will then study continuous paths and loops and introduce the main concept of this module, the Fundamental Group.

Learning outcomes

After this week, you should be able to

  • describe deformation retracts and homotopy, and how they differ from homeomorphisms;
  • list examples of spaces that are homotopy equivalent, and of such that are not;
  • define the fundamental group and show that it is a group;
  • know the fundamental group for some simple examples.

Tasks and Materials

  • Have a look at the lecture notes when they appear.
  • Read pages 1-4 and 25-27 in Hatcher’s book.
  • Have a look at the example sheet published this week. The problems should be handed in on Thursday of Week 3