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School of Environment and Society
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- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Endo Hisaaki
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Mon3-4(H115)
- Group
- -
- Course number
- MTH.B407
- Credits
- 1
- Academic year
- 2019
- Offered quarter
- 3Q
- Syllabus updated
- 2019/3/18
- Lecture notes updated
- -
- Language used
- English
- Access Index
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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 will be succeeded by [MTH.B408 : Advanced topics in Geometry D].
Student learning outcomes
Students are expected to
・understand the definitions of mapping class groups, Dehn twists, and braid groups.
Keywords
Mapping class groups, simple closed curves, Dehn twists, braid groups, Birman's theorem.
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 | Manifolds and isotopies | Details will be provided in class. |
| Class 2 | Connected sums and handle decompositions | Details will be provided in class. |
| Class 3 | Construction and classification of surfaces | Details will be provided in class. |
| Class 4 | Mapping class groups of surfaces | Details will be provided in class. |
| Class 5 | The Dehn-Nielsen-Baer theorem | Details will be provided in class. |
| Class 6 | Curves on surfaces and Dehn twists | Details will be provided in class . |
| Class 7 | Braid groups and Birman's theorem | Details will be provided in class. |
| Class 8 | Evaluation of progress | Details will be provided in class. |
Textbook(s)
None 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 in class.
Related courses
- MTH.B301 ： Geometry I
- MTH.B302 ： Geometry II
- ZUA.B301 ： Geometry I
- MTH.B341 ： Topology
- MTH.B408 ： Advanced topics in Geometry D1
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students are expected to have passed [Geometry I], [Geometry II] and [Topology].
