2025 (Current Year) Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Geometry C1
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Nobuhiro Honda
- Class Format
- Lecture
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Class
- -
- Course Code
- MTH.B407
- Number of credits
- 100
- Course offered
- 2025
- Offered quarter
- 3Q
- Syllabus updated
- Mar 19, 2025
- Language
- English
Syllabus
Course overview and goals
To learn basic properties of the deRham cohomology groups
Course description and aims
・basic properties of the deRham cohomology groups
・calculations of the deRham cohomology groups
・proof of the deRham theorem
Keywords
deRham cohomology group, Stokes theorem, Mayer-Vietoris sequence, Poincare lemma
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Standard lecture course
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Definition and basic examples | Details will be provided in class. |
| Class 2 | deRham cohomology of closed manifold | Details will be provided in class. |
| Class 3 | homotopy principle and Poincare lemma | Details will be provided in class. |
| Class 4 | cochain complex and cohomology group | Details will be provided in class. |
| Class 5 | Mayer-Vietoris exact sequence | Details will be provided in class. |
| Class 6 | deRham theorem 1 | Details will be provided in class . |
| Class 7 | deRham theorem 2 | Details will be provided in class. |
Study advice (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)
No textbook is set.
Reference books, course materials, etc.
Morita Shigeyuki "Geometry of Differential forms" American Mathematical Society
W. Fulton "Algebraic topology, a first course" Springer GTM
C. Taubes "Differential Geometry" Oxford
Evaluation methods and criteria
Assignments (100%).
Related courses
- MTH.B301 ： Geometry I
- MTH.B302 ： Geometry II
- MTH.B331 ： Geometry III
Prerequisites
Assumes understanding of the content of the three courses in Geometry listed above.