Details of MA5207 (Spring 2025)
| Level: 5 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA5207 | Topology and Geometry | Somnath Basu |
| Syllabus |
|---|
| Algebraic Topology: Poincare Duality, Kunneth product formula, universal coefficient theorem.
Differential Topology: Transversality and Morse-Sard theorem, distributions and integrability, Frobenius theorem. Euler Class: Orientation, intersection number, Euler characteristic, Lefschetz fixed point theorem, index of vector field, Poincare-Hopf index theorem, Euler form and Euler class, Euler class of oriented manifolds via Poincare duality. |
| Prerequisite |
|---|
| Prerequisites:
1. Algebra III (MA4101) 2. Representation Theory of Finite Groups (MA4204) 3. Topics in Complex Analysis (MA5106) |
| References |
|---|
| Suggested Texts:
1. Hatcher, A.W., Algebraic Topology, Cambridge University Press. 2. Milnor, J.W. and Stasheff, J., Characteristic Classes, HBA 3. Guillemin, V. and Pollack, A., Differential Topology, Prentice-Hall 4. Hirsch. M., Differential Topology, Springer 5. Bott, R. and Tu, L.W., Differential Forms and Algebraic Topology, Springer |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 2 | Not Allowed |
| 2 | IP | 4 | Not Allowed |
| 3 | IP | 6 | Not Allowed |
| 4 | MP | 2 | Not Allowed |
| 5 | MP | 4 | Not Allowed |
| 6 | MR | 2 | Not Allowed |
| 7 | MR | 4 | Not Allowed |
| 8 | MS | 10 | Elective |
| 9 | MS | 4 | Not Allowed |
| 10 | MS | 6 | Not Allowed |
| 11 | MS | 8 | Not Allowed |
| 12 | RS | 1 | Elective |
| 13 | RS | 2 | Elective |