Lectures on Mapping Class Groups at KAIST
My intention is to talk about basic facts and about spaces on which
mapping class groups act. The following are the major topics I will aim
to cover:
- finite generation by Dehn twists, finite presentability, relations,
...
- pseudo-Anosov homeomorphisms, geodesic laminations, Nielsen-Thurston
classification
- Teichmuller space, curve and arc complex, hyperbolicity
- subsurface projections and a glimpse of the Masur-Minsky theory
There are many good sources for this:
- Farb-Margalit: A primer on mapping
class groups
- Casson-Bleiler: Automorphisms of
surfaces after Nielsen and Thurston
- Minsky: Introduction to mapping
class groups, PCMI notes (download here)
- Ivanov: Mapping class groups,
in Handbook of geometric topology
Prerequisites: In addition to the usual material about covering spaces,
fundamental group, homology (e.g. from Hatcher) and classification of
surfaces (e.g. from Munkres) we will assume familiarity with hyperbolic
geometry (disk or upper half-plane model). I can also review this in
the lectures.
Some sources for hyperbolic geometry:
- Thurston: Three-dimensional
geometry and topology
- Bonahon: Low dimensional geometry
- Cannon-Floyd-Kenyon-Parry: Hyperbolic
geometry (download here)
- Series: Hyperbolic geometry notes
(download here)
As a warmup. here are some homework problems.
Week 1 exercises
Week 2 exercises