The aim of this lecture course is to understand the mapping class group of surfaces via geometry.
During 3Q, we prepare necessary notions(e.g. free groups, Gromov hyperbolic spaces), and then in 4Q, we discuss mapping class groups intensively. This course will be succeeded by [MTH.B404 : Advanced topics in Geometry D].
Study mapping class groups in terms of geometric group theory.
We also understand necessary notions: basics of geometric group theory, geometry of surfaces, etc.
Mapping class groups, hyperbolic geometry, geometric group theory.
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Standard lecture course
Course schedule | Required learning | |
---|---|---|
Class 1 | Basics of hyperbolic planes | Details will be provided during each class session |
Class 2 | Isometry group of the hyperbolic plane | Details will be provided during each class session |
Class 3 | Free groups and generating system of groups | Details will be provided during each class session |
Class 4 | Cayley Graph | Details will be provided during each class session |
Class 5 | Quasi-isometric maps | Details will be provided during each class session |
Class 6 | Gromov hyperbolic spaces | Details will be provided during each class session |
Class 7 | Boundary of Gromov hyperbolic spaces, Ping-Pong Lemma | Details will be provided during each class session |
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
None required
Benson Farb and Dan Margalit, "A Primer on Mapping Class Groups", Princeton Mathematical.
Course notes will be provided.
Evaluation will be based on exams and homework. Details will be provided during class sessions.
Students are expected to have passed [Geometry I], [Geometry II] and [Geometry III].
to be determined