Introduction to algebraic topology (BM)
Collegejaar:  20162017 

Studiegidsnummer:  4373INALG 
Docent(en): 

Voertaal:  Engels 
Blackboard:  Ja 
EC:  6 
Niveau:  400 
Periode:  Semester 2 
 Geen Keuzevak
 Geen Contractonderwijs
 Wel Exchange
 Wel Study Abroad
 Geen Avondonderwijs
 Geen AlaCarte en Aanschuifonderwijs
 Geen Honours Class
Description
In this course we will introduce two ways to study a topological space:
(1) Via coverings and the fundamental group
(2) Via singular homology.
The first part will discuss the SeifertVan Kampen theorem and Galois theory of covering spaces.
We will elaborate on the tight relation between coverings of a given topological space and representations of its fundamental group. This will be done in several level of generality, culminating in Grothendieck’s functorial formulation of Galois theory. We will highlight the similarities with the Galois theory of field extensions.
The second part will treat singular homology and the little homological algebra needed. As applications, we will discuss classical theorems in geometry and topology such as the Brouwer fixed point theorem, the hairy ball theorem, invariance of dimension…
Hours of class per week
2
Final grade
Homework and half an hour oral exam
Prerequisites
Algebra 1 – 3, Lineaire algebra 1 – 2, Topologie
Further information
The course will make use of the language of categories and functors. The basic definitions will be recalled. However a little familiarity with these notions, at level of [this page](https://en.wikipedia.org/wiki/Category_(mathematics) and this page is desirable.
Maakt deel uit van  Soort opleiding  Semester  Blok 

Mathematics  Master  2  
Wiskunde  Bachelor  2 