Details of MA4103 (Autumn 2012)
| Level: 4 | Type: Theory | Credits: 3.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA4103 | Algebraic Topology | Veerendra Vikram Awasthi |
| Syllabus |
|---|
| MA4103 : Algebraic Topology Homotopy Theory: Homotopy and homotopy equivalence; retraction, deformation retract, contractible spaces; fundamental groups; covering spaces, path lifting and homotopy lifting; fundamental group of S1; Borsuk-Ulam theorem, Van-Kampen theorem; fundamental group of Sn; Brouwers no-retraction and fixed point theorem in dimension two. Homology Theory: Barycentric subdivision; finite simplicial complexes and their geometric realizations; simplicial approximation theorem; triangulable spaces, triangulation of standard manifolds; simplicial chain complex, simplicial homology; computation of simplicial homology groups of Sn, RPn and Klein bottle. |
| References |
|---|
| Suggested Texts/Reference Books: 1. Massey, W. S., A Basic Course in Algebraic Topology, Springer-Verlag, 1991. 2. Munkres, J. R., Elements of Algebraic Topology, Addison-Wesley, 1984. 3. Spanier, E. H., Algebraic Topology, Springer-Verlag, 1966. |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 1 | Not Allowed |
| 2 | IP | 3 | Not Allowed |
| 3 | MS | 7 | Not Allowed |
| 4 | RS | 1 | Not Allowed |