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
Homework and oral
Algebra 1—3, Lineaire algebra 1—2, Topologie
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.