MATH701 HOMOTOPY THEORY
| Course Code: | 2360701 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Assoc.Prof.Dr. MEHMET FIRAT ARIKAN |
| Offered Semester: | Fall Semesters. |
Course Objectives
This course provides students with a solid working knowledge in the basic techniques of Homotopy Theory and constitutes a natural continuation of the Math 537-538 sequences in Algebraic Topology. Topics will center around properties and calculations with higher homotopy groups as well as the more general theory of fibrations and fiber bundles. The course should be of interest to all students with research interests in topology or geometry. Topics are; Homotopy groups, Whitehead's theorem, CW approximation; homotopy excision, Hurewicz theorem; (co)fibrations, mapping path and loop spaces; fibre bundles, sphere bundles over spheres; obstruction theory, relation to cohomology; Postnikov towers.
Course Content
Courses not listed in catalogue. Contents vary from year to year according to interest of students and instructor in charge. Typical contents include contemporary developments in Algebra, Analysis, Geometry, Topology, Applied Mathematics.
Course Learning Outcomes
By the end of the course, the student must be able to:
- Manipulate fibrations and cofibrations
- Perform elementary computations of homotopy groups
- Compare homotopy with homology groups
- Define the notions introduced in the course
- State the main theorems and prove them
- Apply the tools developed in the course to examples
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Acquires mathematical thinking skills (problem solving, generating ways of thinking, forming correspondence, generalizing etc.) and can use them in related fields. | ✔ | |||
| 2 | Gains academic maturity through self-study. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Carries out parts of a mathematical research program independently. | ✔ | |||
| 5 | Has a command of Turkish and English languages so that he/she can actively communicate (read, write, listen and speak). | ✔ | |||
| 6 | Contributes to solving global, environmental and social problems either individually or as being part of a social group. | ✔ | |||
| 7 | Respects ethical values and rules; applies them in professional and social issues. | ✔ | |||
| 8 | Can work cooperatively in a team and also individually. | ✔ | |||
| 9 | Gets exposed to academic culture through interaction with others. | ✔ | |||
| 10 | Comprehends necessity of knowledge, can define it and acquires it; uses knowledge effectively and shares it with others. | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution