The aim of this course is to give an introduction to low-dimensional topology.
The objects we study are one- two- and three-dimensional topological manifolds,
their symmetries and the ways in which they embed in each other.
Particular topics we cover are the topological classification of compact surfaces,
knot theory and classical knot invariants such as colourability, the signature or the Alexander polynomial,
the mapping class group, and the Lickorish-Wallace theorem which states
that a compact 3-manifold can be obtained by surgery on a link in the three-dimensional sphere.
(Image by Sam Derbyshire CC BY-SA 4.0)
- Enseignant·e: Livio Liechti