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- Academic unit or major
- Mathematics
- Instructor(s)
- Endo Hisaaki
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Mon3-4(H115)
- Group
- -
- Course number
- ZUA.B334
- Credits
- 1
- Academic year
- 2019
- Offered quarter
- 4Q
- Syllabus updated
- 2019/3/18
- Lecture notes updated
- -
- Language used
- English
- Access Index
-
Course description and aims
The aim of this lecture is to familiarize the students with the basic language of
and some fundamental theorems for mapping class groups of surfaces.
This course is a continuation of [ZUA.B333 : Advanced courses in Geometry C].
Student learning outcomes
Students are expected to
・understand proofs of fundamental theorems on mapping class groups.
Keywords
The Dehn-Lickorish theorem, Lickorish-Humphries generators, Torelli groups, Johnson homomorphisms.
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 | Properties of Dehn twists | Details will be provided during each class session |
| Class 2 | Lickorish generators | Details will be provided during each class session |
| Class 3 | The Dehn-Lickorish theorem (1) | Details will be provided during each class session |
| Class 4 | The Dehn-Lickorish theorem (2) | Details will be provided during each class session |
| Class 5 | Finite presentations of mapping class groups | Details will be provided during each class session |
| Class 6 | Siegel modular groups and Torelli groups | Details will be provided during each class session |
| Class 7 | Johnson homomorphisms | Details will be provided during each class session |
| Class 8 | Evaluation of progress | Details will be provided during each class session |
Textbook(s)
Non required
Reference books, course materials, etc.
B. Farb and D. Margalit, A Primer on Mapping Class Groups, Princeton University Press.
Assessment criteria and methods
Exams and reports. 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].
