2022 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Geometry D
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Hidetoshi Masai
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Mon (H115)
- Class
- -
- Course Code
- MTH.B404
- Number of credits
- 100
- Course offered
- 2022
- Offered quarter
- 4Q
- Syllabus updated
- Jul 10, 2025
- Language
- English
Syllabus
Course overview and goals
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 is a continuation of [MTH.B403 : Advanced topics in Geometry C].
Course description and aims
Study mapping class groups in terms of geometric group theory.
We also understand necessary notions: basics of geometric group theory, geometry of surfaces, etc.
Keywords
Mapping class groups, hyperbolic geometry, geometric group theory.
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Standard lecture course
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Definition and basics of mapping class groups | Details will be provided during each class session |
| Class 2 | Nielsen-Thurston classification | Details will be provided during each class session |
| Class 3 | Complexes related to the mapping class group： curve complex、arc complex、pants graph、flip graph etc. （part 1） | Details will be provided during each class session |
| Class 4 | Complexes related to the mapping class group： curve complex、arc complex、pants graph、flip graph etc. （part 2） | Details will be provided during each class session |
| Class 5 | Gromov hyperbolicity of curve complexes | Details will be provided during each class session |
| Class 6 | Subgroups of mapping class groups(part 1) | Details will be provided during each class session |
| Class 7 | Subgroups of mapping class groups(part 2) | Details will be provided during each class session |
Study advice (preparation and review)
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.
Textbook(s)
None required
Reference books, course materials, etc.
Benson Farb and Dan Margalit, "A Primer on Mapping Class Groups", Princeton Mathematical.
Course notes will be provided.
Evaluation methods and criteria
Evaluation will be based on exams and homework. Details will be provided during class sessions.
Related courses
- MTH.B301 ： Geometry I
- MTH.B302 ： Geometry II
- MTH.B331 ： Geometry III
- MTH.B403 ： Advanced topics in Geometry C
Prerequisites
Students are expected to have passed [Advanced topics in Geometry C]