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

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