The aim of this course is to give an introduction to surface mapping class groups, mingling algebraic, topological and geometric aspects of the theory.
Particular topics of the lecture include: curves on surfaces and intersection numbers, Dehn twists, generating the mapping class group, the Lickorish-Wallace theorem (stating that a compact 3-manifold can be obtained by surgery on a link in the three-dimensional sphere), the Dehn-Nielsen-Baer theorem (relating the mapping class group with the outer automorphisms of the fundamental group), pseudo-Anosov theory.
The image for this course is taken from Thurston's research announcement about his pioneering work on surface diffeomorphisms.
- Enseignant·e: Livio Liechti