Course content

The course covers advanced topics in topology that are not covered by the other courses. For instance: vector bundles, topological and/or algebraic K-theory, Morse theory, bordism theory, spectra and stable homotopy theory, homotopical and higher algebra.

Learning outcome

1. Knowledge. The student can give the definitions of the key concepts, state and prove the main theorems, and work out key examples from the topic covered in the course. 2. Skills. The student is ready to conduct research in topology and to apply ideas from topology in other areas of mathematics and beyond.

Learning methods and activities

The learning methods and activities depend on the lecturer. The course may be taught in English.

The course will be taught as needed. If there are few PhD students, the course is only given as a guided self-study.

Recommended previous knowledge

Depends on the specific topic, but the course will usually at least be based on TMA4190 Introduction to Topology, MA3403 Algebraic Topology 1, and MA3408 Algebraic Topology 2.

Course materials

Given at beginning of course.