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: | Prof.Dr. MUSTAFA TURGUT ÖNDER |
| 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