In this course we will treat 2 important methods/techniques in topology and geometry: (1) singular homology, (2) sheaves and cohomology. Both are aimed at understanding the global properties of a topological space by analyzing how the space is built up out of simple pieces. We shall try to emphasise both formal/abstract properties and concrete examples. Part (1) will end with a discussion of the Brouwer fixpoint theorem in arbitrary dimension, and the hairy ball theorem.

**Hours of class per week**

2

**Final grade**

Homework and oral

**Prerequisites**

Algebra 1—3, Lineaire algebra 1—2, Topologie

**Further information:**

Homepage

If time permits, we will elaborate on the tight relation between the category of covering spaces of a given path connected space X, on the one hand, and the category of representations of the fundamental group of X, on the other.