M2: Algebraic Topology 2 - 8EC

Prerequisites

  • Point set topology and the fundamental group
  • CW-complexes and singular homology (to the extent treated in the Algebraic Topology course taught in the fall)

Aim of the course

This course covers advanced topics in Algebraic Topology which vary from year to year and build on the foundations provided by the Algebraic Topology course from the fall.
The main subject of this edition of Algebraic Topology II is the study of cohomology groups of topological spaces. In the first part, we will construct the singular cohomology groups of topological spaces and the cup-product. In the second part, we will explain how singular cohomology can be viewed as a special case of a generalized cohomology theory. We will also cover foundations from homotopy theory such as Eilenberg-Mac Lane spaces that are needed for this.

Rules about Homework / Exam

The type of examination will depend on the number of students taking the exam. Most likely, there will be a written exam, with a bonus for exercises.

    Lecture Notes / Literature

    Parts of this course are covered by standard textbooks on AlgebraicTopology:

    • Glen E. Bredon, Topology and Geometry
    • Allen Hatcher, Algebraic Topology
    • Tammo tom Dieck, Algebraic Topology

    We will provide additional references during the course. 

    Lecturers

    G. Heuts (UU) & S. Sagave (RU)