Course content

The aim of the course is to show how basic geometric structures may be studied by transforming them into algebraic questions that are then subject to computations, thus measuring geometric and topological complexity. These methods are often used in other parts of mathematics, and also in biology, physics and other areas of application. The course is meant to give a basis for studies in topology, geometry, algebra, and applications. An introduction to category theory, homotopy theory, simplicial methods, homology theory and products is given, along with specific examples of computations.

Learning outcome

1. Knowledge. The student has knowledge of fundamental concepts and methods in algebraic topology, in particular singular homology and cohomology theory.

2. Skills. The student is able to apply his or her knowledge of algebraic topology to formulate and solve problems of a geometric-topological nature in mathematics and its applications.

Learning methods and activities

Lectures and project/term paper. Oral exam which counts 100 %. The lectures will be given in English if the course is attended by students who don't master a Scandinavian language.

Recommended previous knowledge

MA3002 General Topology,
MA3402 Analysis on Manifolds or
TMA4190 Introduction to Topology, and
MA3201 Rings and Modules or
MA3204 Homological Algebra.

Course materials

Will be announced at the start of the course.

Credit reductions