▶Japanese
Post to SNS
- Home
- > School of Science
- > Graduate major in Mathematics
- > Advanced topics in Geometry H1
- 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)
- Nosaka Takefumi
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Fri5-6(H119A)
- Group
- -
- Course number
- MTH.B508
- Credits
- 1
- Academic year
- 2017
- Offered quarter
- 4Q
- Syllabus updated
- 2017/8/21
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
In application, group cohomology appears in number theory, low dimensional topology, algebraic K-theory, and on. In this course, I introduce some applications of group cohomology. For example, I discuss Massey products, scissors congruence, stability and (secondary) characteristic classes. This course is continued on the previous "G1"course.
Student learning outcomes
The aim is to understand topological applications of group cohomology. I plan to introduce Massey product, low dimensional topology, Dickson polynomial, and characteristic classes.
Keywords
Group cohomology, fundamental group, covering of CW complexes, central extension, cup products, and (Secondary) characteristic classes
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
A common course
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Massey products and nilpotent groups | Definitions and properties |
| Class 2 | Massey products, Milnor invariant, and Johnson homomorphism. | Definitions and properties |
| Class 3 | Some applications of group cohomology to low dimensional topology | Definitions and properties |
| Class 4 | Survey of Chern class and Dickson invariants | Definitions and properties |
| Class 5 | Examples of cocycles | Definitions and properties |
| Class 6 | Simplicial manifolds and (Secondary) characteristic classes | Definitions and properties |
| Class 7 | An expression of Chern-Simons 2-class. | Definitions and properties |
| Class 8 | Extended Bloch group, hyperbolic volume, Algebraic K theory. | Definitions and properties |
Textbook(s)
No textbook
Reference books, course materials, etc.
K. S. Brown 「Cohomology of groups 」
Dupont, 「Curvature and Characteristic Classes 」
Assessment criteria and methods
Reports
Related courses
- MTH.B202 ： Introduction to Topology II
- MTH.B301 ： Geometry I
- MTH.B302 ： Geometry II
Prerequisites (i.e., required knowledge, skills, courses, etc.)
I suppose elementary and basics on group and topology.
Other
It is important to complete the previous college course on this topic.
I welcome any questions on this course.
