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- Academic unit or major
- Mathematics
- Instructor(s)
- Masai Hidetoshi
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- Day/Period(Room No.)
- Mon3-4(H115)
- Group
- -
- Course number
- ZUA.B334
- Credits
- 1
- Academic year
- 2022
- Offered quarter
- 4Q
- Syllabus updated
- 2022/4/20
- Lecture notes updated
- -
- Language used
- English
- Access Index
-
Course description and aims
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 [ZUA.B333 : Advanced courses in Geometry C].
Student learning outcomes
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 that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
Standard lecture course
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| 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 |
Out-of-Class Study Time (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.
Assessment criteria and methods
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
- ZUA.B301 ： Geometry I
- MTH.B341 ： Topology
- ZUA.B333 ： Advanced courses in Geometry C
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students are expected to have passed [Geometry I], [Geometry II], [Topology] and [Advanced courses in Geometry C].
