Introduction to the Mapping Class Group
The mapping class group of a surface S, denoted by MCG(S), is the
group of homeomorphisms of S up to isotopy (i.e. homotopy through
homeomorphisms). This group is a fundamental object in low dimensional
topology. For instance, two of the easiest ways to build 3-manifolds
are encoded by elements of the mapping class group:
Heegaard splittings and suspensions of diffeomorphisms.
The study of the mapping class group is very active since the work
of Thurston in the 80's.
The course will cover the following topics: finite subgroups of MCG(S),
curve complex, generating sets, torsion free subgroups, Torelli group.
This course requires a basic knowledge in topology, there will be some
preliminaries on surfaces (topology, hyperbolic geometry).