▶Japanese
Post to SNS
- Home
- > School of Science
- > Graduate major in Mathematics
- > Advanced topics in Geometry G
- School of Science
-
School of Engineering
- Undergraduate major in Mechanical Engineering
- Undergraduate major in Systems and Control Engineering
- Undergraduate major in Electrical and Electronic Engineering
- Undergraduate major in Information and Communications Engineering
- Undergraduate major in Industrial Engineering and Economics
- Common courses
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
- School of Environment and Society
- 工学院，物質理工学院，環境・社会理工学院共通科目
- Liberal arts and basic science courses
- First-Year Courses
- School of Science
- School of Engineering
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
-
School of Environment and Society
- Department of Architecture and Building Engineering
- Department of Civil and Environmental Engineering
- Department of Transdisciplinary Science and Engineering
- Department of Social and Human Sciences
- Department of Innovation Science
- Graduate major in Technology and Innovation Management
- Common courses
- 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.)
- -
- Group
- -
- Course number
- MTH.B503
- Credits
- 1
- Academic year
- 2024
- Offered quarter
- 3Q
- Syllabus updated
- 2024/3/14
- 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 Lefschetz fibrations on 4-manifolds. This course will be succeeded by [MTH.B504 : Advanced topics in Geometry H].
Student learning outcomes
Students are expected to
・understand the definitions of Lefschetz fibrations, monodromy representations and Hurwitz systems.
Keywords
4-manifolds, Lefschetz fibrations, monodromy representations, Hurwitz systems, mapping class groups, signatures
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 | 4-manifolds and their intersection forms | Details will be provided in class. |
| Class 2 | Definition of Lefschetz fibrations | Details will be provided in class. |
| Class 3 | Singular fibers and their neighborhoods | Details will be provided in class. |
| Class 4 | Monodromy representations and classification theorems | Details will be provided in class. |
| Class 5 | Hurwitz systems and elementary transformations | Details will be provided in class. |
| Class 6 | Meyer's signature cocycle and local signatures | Details will be provided in class. |
| Class 7 | Relators in mapping class groups and their signatures | Details will be provided in class. |
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 contents afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
None
Reference books, course materials, etc.
R. I. Gompf and A. I. Stipsicz, 4-Manifolds and Kirby Calculus, American Mathematical Society, 1999.
H. Endo and K. Hayano, 4-manifolds and fibrations, in Japanese, Kyoritsu Shuppan, 2024.
Assessment criteria and methods
Homework assignments (100％)
Related courses
- MTH.B301 ： Geometry I
- MTH.B202 ： Introduction to Topology II
- MTH.B302 ： Geometry II
- MTH.B341 ： Topology
- MTH.B504 ： Advanced topics in Geometry H
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Basic algebraic topology (homology, cohomology, and the fundamental group) and smooth manifolds.
Other
To be announced.
