Special Topics in Topology

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.

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.

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.