Details of MA4104 (Autumn 2025)
| Level: 4 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA4104 | Algebraic Topology | Sushil Gorai |
| Syllabus |
|---|
| Fundamental Group: Review of quotient topology, path homotopy, definition of fundamental group, covering spaces, path and homotopy lifting, fundamental group of $S^1$, deformation retraction, Brouwer's fixed point theorem, Borsuk-Ulam theorem, van-Kampen's theorem, fundamental group of surfaces, universal covering space, correspondence between covering spaces and subgroups of fundamental group.
Homology Theory: Simplicial complexes and maps, homology groups, computation for surfaces. |
| Prerequisite |
|---|
| Algebra I (MA3102) and Topology (MA3201) |
| References |
|---|
| Suggested Texts:
1. Hatcher, A., Algebraic Topology, Cambridge University Press. 2. Massey, W.S., A Basic Course in Algebraic Topology, Springer-Verlag. 3. Munkres, J.R., Elements of Algebraic Topology, Addison-Wesley. 4. Spanier, E.H., Algebraic Topology, Springer-Verlag. |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 1 | Not Allowed |
| 2 | IP | 3 | Not Allowed |
| 3 | IP | 5 | Not Allowed |
| 4 | MP | 1 | Not Allowed |
| 5 | MP | 3 | Core |
| 6 | MR | 1 | Not Allowed |
| 7 | MR | 3 | Not Allowed |
| 8 | MS | 3 | Not Allowed |
| 9 | MS | 5 | Not Allowed |
| 10 | MS | 7 | Elective |
| 11 | MS | 9 | Elective |
| 12 | RS | 1 | Elective |
| 13 | RS | 2 | Elective |