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- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- -
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Intensive ()
- Group
- -
- Course number
- MTH.E443
- Credits
- 1
- Academic year
- 2019
- Offered quarter
- 1Q
- Syllabus updated
- 2019/3/18
- Lecture notes updated
- -
- Language used
- English
- Access Index
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Course description and aims
In the early 1920s M. Morse discovered that the number of critical points of a smooth function on a manifold is closely related to the topology of the manifold. This became a starting point of the Morse theory which is now one of the basic parts of differential topology.
Circle-valued Morse theory originated from a problem in hydrodynamics studied by S. P. Novikov in the 1980s. Nowadays, it is a constantly growing field of contemporary mathematics with applications and connections to many domains of geometry and topology.
The aim of this course is to give a systematic treatment of geometric foundations of the subject and recent research results.
Student learning outcomes
Students will be able to understand basics of Morse theory and circle-valued Morse theory.
Keywords
Morse theory, circle-valued Morse theory
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 | This course covers the fundamentals of Morse theory and circle-valued Morse theory and several topics such as: - Homology with local coefficients for the Morse-Novokov theory; - The Morse-Novikov theory for closed 1-forms; - Circle-valued Morse theory for knots and links, etc. | Details will be provided in class. |
Textbook(s)
None required
Reference books, course materials, etc.
A. V. Pajitnov, Circle-valued Morse Theory, Walter de Gruyter.
Assessment criteria and methods
Assignments (100%).
Related courses
- MTH.B301 ： Geometry I
- MTH.B302 ： Geometry II
- MTH.B331 ： Geometry III
- MTH.B341 ： Topology
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students require the knowledge of manifolds and homology.
Other
None
