Mapping class groups

Here are hand-written notes from the course.

This was a course on mapping class groups of surfaces. Topics included:

1. Algebraic structure of mapping class groups
   • finite generation
   • presentation
   • abelianization
2. Surface bundles
   • Over the circle: multiple fiberings, Thurston norm
   • Over surfaces: signature, Atiyah–Kodaira examples, surface subgroups of Modg
   • Characteristic classes: Miller–Morita–Mumford classes
3. Mumford conjecture.
   • Harer’s homological stability theorem
   • Madsen–Weiss theorem
   • Homotopy type of diffeomorphism groups, Earle–Eells theorem
4. Lifting problems for Mod_g
   • Morita’s nonlifting theorem, flat connections on surface bundles
   • Lifting problems for surface braid groups