# Introduction to Algebraic Topology (Part-II)

- Institution: IIT Bombay
- Department: Mathematics
- Teacher: Prof. Anant R. Shastri
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111101152)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111101152)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Week 1-Lecture 1 : Introduction](https://invisiblenetwork.ai/learn/nptel/111101152/233cf8c99d31) (Video)
2. [Week 1-Lecture 2 : Attaching cells](https://invisiblenetwork.ai/learn/nptel/111101152/cb020e6826dd) (Video)
3. [Week 1-Lecture 3 : Subcomplexes and Examples](https://invisiblenetwork.ai/learn/nptel/111101152/3762132c6df0) (Video)
4. [Week 1-Lecture 4A : More examples](https://invisiblenetwork.ai/learn/nptel/111101152/f735a7aa52c6) (Video)
5. [Week 1-Lecture 4B : More Examples](https://invisiblenetwork.ai/learn/nptel/111101152/958313d88fa7) (Video)
6. [Weeek 1-Lecture 5 : Topological Properties](https://invisiblenetwork.ai/learn/nptel/111101152/c12b4056a1c6) (Video)
7. [Week 2-Lecture 6 : Coinduced Topology](https://invisiblenetwork.ai/learn/nptel/111101152/5f2ec560bfdc) (Video)
8. [Week 2-Lecture 7 : Compactly generated topology on Products](https://invisiblenetwork.ai/learn/nptel/111101152/9f55b394becb) (Video)
9. [Week 2-Lecture 8 : Product of Cell complexes](https://invisiblenetwork.ai/learn/nptel/111101152/1e846fa72068) (Video)
10. [Week 2-Lecture 9 : Product of Cell complexes-Continued](https://invisiblenetwork.ai/learn/nptel/111101152/b4137a76e1e2) (Video)
11. [Week 2-Lecture 10 : Partition of Unity on CW-complexes](https://invisiblenetwork.ai/learn/nptel/111101152/e0586113e652) (Video)
12. [Week 3-Lecture 11 : Partition of Unity-Continued](https://invisiblenetwork.ai/learn/nptel/111101152/b9a730b9f3a3) (Video)
13. [Week 3-Lecture 12 : Homotopical Aspects](https://invisiblenetwork.ai/learn/nptel/111101152/377ad70c8c48) (Video)
14. [Week 3-Lecture 13 : Homotopical Aspects-Continued](https://invisiblenetwork.ai/learn/nptel/111101152/131752c0ae25) (Video)
15. [Week 3-Lecture 14 : Cellular Maps](https://invisiblenetwork.ai/learn/nptel/111101152/6ed45e643948) (Video)
16. [Week 3-Lecture 15 : Cellular Maps-Continued](https://invisiblenetwork.ai/learn/nptel/111101152/957fde3d7a28) (Video)
17. [Week 4-Lecture 16A : Homotopy exact sequence of a pair](https://invisiblenetwork.ai/learn/nptel/111101152/f7ef23b9dc6c) (Video)
18. [Week 4-Lecture 16B : Homotopy exact sequence of a fibration](https://invisiblenetwork.ai/learn/nptel/111101152/a4710ddf9d89) (Video)
19. [Week 4-Lecture 17 : Categories-Definitions and Examples](https://invisiblenetwork.ai/learn/nptel/111101152/7d23648d2df3) (Video)
20. [Week 4-Lecture 18 : More Examples](https://invisiblenetwork.ai/learn/nptel/111101152/6cab5e2807c4) (Video)
21. [Week 4-Lecture 19 : Functors](https://invisiblenetwork.ai/learn/nptel/111101152/4e6f440f6344) (Video)
22. [Week 4-Lecture 20 : Equivalence of Functors-Continued](https://invisiblenetwork.ai/learn/nptel/111101152/6cb650eddaff) (Video)
23. [Week 5-Lecture 21 : Universal Objects](https://invisiblenetwork.ai/learn/nptel/111101152/d39dfa51341d) (Video)
24. [Week 5-Lecture 22 : Basic Homological Algebra](https://invisiblenetwork.ai/learn/nptel/111101152/062f1ea95085) (Video)
25. [Week 5-Lecture 23 : Diagram-Chasing](https://invisiblenetwork.ai/learn/nptel/111101152/7c075c029b6e) (Video)
26. [Week 5-Lecture 24 : Homology of Chain Complexes](https://invisiblenetwork.ai/learn/nptel/111101152/4e7028d08cf2) (Video)
27. [Week 5-Lecture 25 : Euler Characteristics](https://invisiblenetwork.ai/learn/nptel/111101152/6fb0a30afb93) (Video)
28. [Week 6-Lecture 26 : Singular Homology Groups](https://invisiblenetwork.ai/learn/nptel/111101152/f53334288c40) (Video)
29. [Week 6-Lecture 27 : Basic Properties of Singular Homology](https://invisiblenetwork.ai/learn/nptel/111101152/36c0727339ec) (Video)
30. [Week 6-Lecture 28 : Excision](https://invisiblenetwork.ai/learn/nptel/111101152/f3656de898c1) (Video)
31. [Week 6-Lecture 29 : Examples of Excision-Mayer Vietoris](https://invisiblenetwork.ai/learn/nptel/111101152/02f58c96ff2f) (Video)
32. [Week 6-Lecture 30 : Applications](https://invisiblenetwork.ai/learn/nptel/111101152/8c656e088023) (Video)
33. [Week 7-Lecture 31 : Applications-Continued](https://invisiblenetwork.ai/learn/nptel/111101152/574e49b7819c) (Video)
34. [Week 7-Lecture 32 : The Singular Simplicial Homology](https://invisiblenetwork.ai/learn/nptel/111101152/580e9d608300) (Video)
35. [Week 7-Lecture 33 : Simplicial Homology](https://invisiblenetwork.ai/learn/nptel/111101152/81f3d928cc03) (Video)
36. [Week 7-Lecture 34 : Simplicial Homology-Continued](https://invisiblenetwork.ai/learn/nptel/111101152/46db781df416) (Video)
37. [Week 7-Lecture 35 : CW-Homology and Cellular Singular Homology](https://invisiblenetwork.ai/learn/nptel/111101152/6de7d728372a) (Video)
38. [Week 8-Lecture 36 : Construction of CW-chain complex](https://invisiblenetwork.ai/learn/nptel/111101152/8cdf51eba1e8) (Video)
39. [Week 8-Lecture 37 : CW structure and CW homology of Lens Spaces](https://invisiblenetwork.ai/learn/nptel/111101152/ab708ffef748) (Video)
40. [Week 8-Lecture 38 : Assorted Topics](https://invisiblenetwork.ai/learn/nptel/111101152/419d23fea1da) (Video)
41. [Week 8-Lecture 39 : Some Applications of Homology](https://invisiblenetwork.ai/learn/nptel/111101152/cf4679cbbf12) (Video)
42. [Week 8-Lecture 40 : Applications of LFT](https://invisiblenetwork.ai/learn/nptel/111101152/b7145bbcac50) (Video)
43. [Week 9-Lecture 41 : Jordan-Brouwer](https://invisiblenetwork.ai/learn/nptel/111101152/372bf03825f4) (Video)
44. [Week 9-Lecture 42 : Proof of Lemmas](https://invisiblenetwork.ai/learn/nptel/111101152/7a30bbff11d0) (Video)
45. [Week 9-Lecture 43 : Relation between ?1 and H1](https://invisiblenetwork.ai/learn/nptel/111101152/953f7145b091) (Video)
46. [Week 9-Lecture 44 : All Postponed Proofs](https://invisiblenetwork.ai/learn/nptel/111101152/a5be98129047) (Video)
47. [Week 9-Lecture 45 : Proofs-Continued](https://invisiblenetwork.ai/learn/nptel/111101152/e62e718c3211) (Video)
48. [Week 10-Lecture 46 : Definitions and Examples](https://invisiblenetwork.ai/learn/nptel/111101152/9022068f158f) (Video)
49. [Week 10-Lecture 47 : Paracompactness](https://invisiblenetwork.ai/learn/nptel/111101152/214c07f18521) (Video)
50. [Week 10-Lecture 48 : Manifolds with Boundary](https://invisiblenetwork.ai/learn/nptel/111101152/ac5506202fe6) (Video)
51. [Week 10-Lecture 49 : Embeddings and Homotopical Aspects](https://invisiblenetwork.ai/learn/nptel/111101152/f95cad78178a) (Video)
52. [Week 10-Lecture 50 : Homotopical Aspects continued](https://invisiblenetwork.ai/learn/nptel/111101152/cfc8ecda7d58) (Video)
53. [Week 11-Lecture 51 : Classification of 1-manifolds](https://invisiblenetwork.ai/learn/nptel/111101152/f9f2a9ee7c4a) (Video)
54. [Week 11-Lecture 52 : Classification of 1-manifolds-continued](https://invisiblenetwork.ai/learn/nptel/111101152/f0b747c30b44) (Video)
55. [Week 11-Lecture 53 : Triangulation of Manifolds](https://invisiblenetwork.ai/learn/nptel/111101152/26b9eec5e53b) (Video)
56. [Week 11-Lecture 54 : Pseudo-Manifolds](https://invisiblenetwork.ai/learn/nptel/111101152/c9bbb836f009) (Video)
57. [Week 11-Lecture 55 : One result due to Poincaŕe and another due to Munkres](https://invisiblenetwork.ai/learn/nptel/111101152/afc6d50f8dcf) (Video)
58. [Week 12-Lecture 56 : Some General Remarks](https://invisiblenetwork.ai/learn/nptel/111101152/53f833b7e820) (Video)
59. [Week 12-Lecture 57 : Classification of Compact Surface](https://invisiblenetwork.ai/learn/nptel/111101152/e629c22eee17) (Video)
60. [Week 12-Lecture 58 : Final Reduction-Completion of the Proof](https://invisiblenetwork.ai/learn/nptel/111101152/876d518e09e1) (Video)
61. [Week 12-Lecture 59 : Proof of Part B](https://invisiblenetwork.ai/learn/nptel/111101152/4d3254a00a7e) (Video)
62. [Week 12-Lecture 60 : Orientability](https://invisiblenetwork.ai/learn/nptel/111101152/58ba5079e68a) (Video)