MATH541 DIFFERENTIAL TOPOLOGY
| Course Code: | 2360541 |
| 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: | |
| Offered Semester: | Fall Semesters. |
Course Objectives
At the end of the course the student will know
- basic notions and techniques about the topology of manifolds like transversality techniques,
- basic theorems of differential topology like Whitney Embedding Theorem, Sards Theorem, Transversality Homotopy Theorem etc.,
- some applications of transversality like Intersection Theory.
Course Content
Manifolds and differentiable structures. Tangent Space. Vector bundles. Immersions, submersions, embeddings. Transversality. Sard's theorem. Whitney Embedding Theorem. The exponential map and tubular neighborhoods. Manifolds with boundary. Thom's tranversality Theorem.