Entry requirements

Riemannian Geometry. The course Modules and Homological Algebra is highly recommended but not necessary.

Learning outcomes

In order to pass the course (grade 3) the student should be able to

• give an account of the concepts homotopy, homology and cohomology, their basic properties and relationships;
• compute algebro-topological invariants in specific examples;
• use the theory to solve elementary topological problems;
• give an account of fundamental topological examples, e.g. surfaces, knots, classical Lie-groups, Grassmannian manifolds, configuration rooms.

Content

The fundamental group and covering spaces, singular and cellular homology, the Mayer-Vietoris sequence, cohomology, the universal coefficient theorem, the Künneth theorem, the Cup product, Poincaré duality, homotopy groups, the Hurewicz and Whitehead theorems, Eilenberg-MacLane spaces, obstruction theory.

Instruction

Lectures and problem solving sessions.

Assessment

Written examination and assignments during the course.

Other directives

The course cannot be included in passing degree together with the course Topology II.