| Date | Lecture topics | Comments | |
|---|---|---|---|
| L1 | 5 Apr (M) | Introduction | |
| L2 | 6 Apr (Tu) | Quotient Topology | Munkres, Ch-2 §-22. |
| L3 | 8 Apr (Th) | CW complexes | Hatcher, Ch-0. |
| L4 | 9 Apr (F) | Deformation retraction and Homotopy of maps | Hatcher, Ch-0. |
| L5 | 12 Apr (M) | Homotopy equivalence, Contractible spaces. | Hatcher, Ch-0. |
| P1 | 13/4, Tu | Problem session. | PS-1 |
| L6 | 15 Apr (Th) | Path homotopy and Fundamental group | Hatcher, §-1.1. |
| L7 | 16 Apr (F) | Properties of the fundamental group, Induced homomorphism. | Hatcher, §-1.1. |
| L8 | 19 Apr (M) | Properties of the fundamental group, Simply connected spaces. | Hatcher, §-1.1. |
| L9 | 20 Apr (Tu) | S^n is simply connected for n>1, Covering spaces. | Hatcher, §-1.1. |
| L10 | 22 Apr (Th) | Homotopy extension property for covering spaces, Fundamental group of S^1. | Hatcher, §-1.1. |
| P2 | 23 Apr (F) | Problem Session. | PS-2 |
| L11 | 19 Apr (M) | Applications of the Computation of the fundamental group of the circle. | Hatcher, §-1.1. |
| L12 | 27 Apr (T)u | Free Products of groups. | Massey, Ch-III, §-4. |
| L13 | 29 Apr (Th) | Free Groups and Group Presentations | Massey, Ch-III, §-5,6. |
| L14 | 30 Apr (F) | Van Kampen's theorem. | Hatcher, §-1.2. |
| L15 | 3 May (M) | Applications of Van Kampen's theorem. | Hatcher, §-1.2. |
| L16 | 4 May (Tu) | Fundamental group of a CW Complex. | Hatcher, §-1.2. |
| L17 | 6 May (Th) | Fundamental Group of a knot Compliment. | Massey, Ch-IV §-6. |
| P3 | 7 May (F) | Problem Session | PS-3 |
| P3 | 10 May (M) | Problem Session | PS-3 |
| L18 | 11 May (Tu) | Covering Spaces and lifting properties. | Massy Ch-V, §-2,3. |
| L19 | 13 May (Th) | Covering Spaces and Fundamental group. | Massey, Ch-V §-4. |
| L20 | 28 May (F) | Lifting of Arbitrary Maps to a Cover. | Massey, Ch-V §-5. |
| 30 May (Sun) | Midsem Problems | ||
| L21 | 31 May (M) | Universal Cover | Massey, Ch-V §-10. |
| L21 | 1 June (Tu) | Universal cover continued | Massey, Ch-V §-6. |
| L22 | 3 June (Th) | Covering transformations | Massey, Ch-V §-7. |
| L23 | 4 June (F) | Examples of covers | |
| L24 | 7 June (M) | Group actions associated to a cover | Massey, Ch-V §-7. |
| L25 | 8 June (Tu) | Regular covers and Covering space actions | Massey, Ch-V §-8. |
| L26 | 10 June (Th) | Classification of covering spaces | Massey, Ch-V §-10. |
| P4 | 11 June (F) | Problem session | PS-4 |
| L27 | 14 June (M) | Simplices and Delta Complexes | Hatcher, §-2.1 |
| L28 | 15 June (Tu) | Delta Complexes and Simplicial Homology | Hatcher, §-2.1 |
| L28 | 17 June (Th) | Simplicial Homology and Computations | Hatcher, §-2.1 |
| L29 | 18 June (F) | Singular Homology | Hatcher, §-2.1 |
| L30 | 21 June (M) | Homotopy invariance of singular homomolgy | Hatcher, §-2.1 |
| L31 | 22 June (Tu) | Relative homology Long exact sequence | Hatcher, §-2.1 |
| L32 | 24 June (Th) | Excision and Applications | Hatcher, §-2.1 |
| L33 | 25 June (F) | Mayer Vietoris sequence | Hatcher, §-2.1 |
| L34 | 28 June (M) | Equivalence of Simplicial and Singular Homology | Hatcher, §-2.1 |
| L35 | 29 June (Tu) | Degree | Hatcher, §-2.2 |
| L36 | 1 July (Th) | Homology of a CW complex | Hatcher, §-2.2 |
| L37 | 2 July (F) | Euler Characteristic | Hatcher, §-2.2 |
|
This is a BS/MS third and fourth year course. |
Texts:
- A. Hatcher, Algebraic Topology, available at the author's web page.
- W.S. Massey, A Basic Course in Algebraic Topology.
- Munkres, Topology, Prentice-Hall of India, 2013.
- Munkres, Elements of Algebraic Topology.
Other resources: I came to know of these excellent sets of lectures from Prof. Pranav Haridas at KSOM.
- Lectures on Algebraic Topology by Siddhart Gadgil at IISC Bangalore in Fall 2020.
- Lectures on Algebraic Topology by Pierre Albin at University of Illinois at Urbana-Champaign in Spring 2018.
Problem sets. Please attempt all problems. Collaboration is encouraged.
Exams: Quiz 1 - 3rd May (Monday); Midsem - 23 May (Sunday) 14:30-16:30 hrs; Quiz 2 - 16th June (Wednesday); Final - 13 July (Tuesday) 10:00-13:00 hrs.
Grading percentages: Quizzes - 30%, Midterm - 30%, Final - 40%.
Lecture notes, Video recordings. Please point out any typos or mistakes.
Summary of Lectures: