# Introduction to Algebraic Topology

- Institution: IIT Palakkad
- Department: Mathematics
- Teacher: Prof. Arpan Kabiraj
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106905)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106905)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Basics of Topology](https://invisiblenetwork.ai/learn/nptel/111106905/cc5125d3692e) (Video)
2. [Some Topological Constructions and Homotopy](https://invisiblenetwork.ai/learn/nptel/111106905/ed7cb3635bd0) (Video)
3. [Retraction and Deformation Retraction](https://invisiblenetwork.ai/learn/nptel/111106905/dd00d0726489) (Video)
4. [Contractible Spaces and Null Homotopy](https://invisiblenetwork.ai/learn/nptel/111106905/869d85602a5a) (Video)
5. [Some Questions](https://invisiblenetwork.ai/learn/nptel/111106905/073dbf4ef3ec) (Video)
6. [Simplicial Complex 1](https://invisiblenetwork.ai/learn/nptel/111106905/f059ec6b85d4) (Video)
7. [Simplicial Complex 2](https://invisiblenetwork.ai/learn/nptel/111106905/c4cbb2d12c29) (Video)
8. [Simplicial Complex 3](https://invisiblenetwork.ai/learn/nptel/111106905/f5c484609563) (Video)
9. [Simplicial Complex 3 Delta Complex](https://invisiblenetwork.ai/learn/nptel/111106905/3ac48e877148) (Video)
10. [Path Homotopy](https://invisiblenetwork.ai/learn/nptel/111106905/8d345bfef9b8) (Video)
11. [The Fundamental Group](https://invisiblenetwork.ai/learn/nptel/111106905/51e264816128) (Video)
12. [Covering Spaces](https://invisiblenetwork.ai/learn/nptel/111106905/69ad76d9079e) (Video)
13. [Path Lifting](https://invisiblenetwork.ai/learn/nptel/111106905/e0bf790c724f) (Video)
14. [Homotopy Lifting](https://invisiblenetwork.ai/learn/nptel/111106905/1dca78148d06) (Video)
15. [The Fundamental Group of a Circle](https://invisiblenetwork.ai/learn/nptel/111106905/d7e5b5c7df03) (Video)
16. [The Induced Homomorphism](https://invisiblenetwork.ai/learn/nptel/111106905/eb3255dc948c) (Video)
17. [Applications](https://invisiblenetwork.ai/learn/nptel/111106905/d7597f1bdfc4) (Video)
18. [The Fundamental Group of a Sphere](https://invisiblenetwork.ai/learn/nptel/111106905/71b7a85e6f17) (Video)
19. [Free Product of Groups](https://invisiblenetwork.ai/learn/nptel/111106905/cfc7c577dcb3) (Video)
20. [Seifert–Van Kampen Theorem 1](https://invisiblenetwork.ai/learn/nptel/111106905/00349e193b79) (Video)
21. [Seifert–Van Kampen Theorem 2](https://invisiblenetwork.ai/learn/nptel/111106905/6168e3c940ae) (Video)
22. [Lifting correspondence and Lifting criterion](https://invisiblenetwork.ai/learn/nptel/111106905/3d1fd8cb7553) (Video)
23. [Classification of Covering Spaces 1](https://invisiblenetwork.ai/learn/nptel/111106905/9c23474cec5c) (Video)
24. [Classification of Covering Spaces 2](https://invisiblenetwork.ai/learn/nptel/111106905/466509f857b6) (Video)
25. [Classification of Covering Spaces 3](https://invisiblenetwork.ai/learn/nptel/111106905/516764ac5270) (Video)
26. [The Group of Deck transformations](https://invisiblenetwork.ai/learn/nptel/111106905/f79b6b254d4e) (Video)
27. [Action of Deck Transformations](https://invisiblenetwork.ai/learn/nptel/111106905/a2368356f55d) (Video)
28. [Graphs and Free Groups](https://invisiblenetwork.ai/learn/nptel/111106905/e2f30d8a8522) (Video)
29. [Free modules and chain complexes](https://invisiblenetwork.ai/learn/nptel/111106905/d4b5fbfc3e30) (Video)
30. [Notation and conventions](https://invisiblenetwork.ai/learn/nptel/111106905/c4e2dca96292) (Video)
31. [The Simplicial Chain Complex](https://invisiblenetwork.ai/learn/nptel/111106905/ca79b724bed2) (Video)
32. [Simplicial Homology : Examples](https://invisiblenetwork.ai/learn/nptel/111106905/0b711f5b182c) (Video)
33. [Few results about Homology](https://invisiblenetwork.ai/learn/nptel/111106905/f8301c19eda6) (Video)
34. [Relative Homology](https://invisiblenetwork.ai/learn/nptel/111106905/825cdb3b44c9) (Video)
35. [Induced homomorphism 01](https://invisiblenetwork.ai/learn/nptel/111106905/618792cd6c48) (Video)
36. [Induced homomorphism 02 Homology of a cone](https://invisiblenetwork.ai/learn/nptel/111106905/92daa26191ff) (Video)
37. [Induced homomorphism 03 Contiguous maps](https://invisiblenetwork.ai/learn/nptel/111106905/2cc367224e3d) (Video)
38. [Induced homomorphism 04 Simplicial approximations and barycentric subdivisions](https://invisiblenetwork.ai/learn/nptel/111106905/d3e214a4b593) (Video)
39. [Induced homomorphism 05 Invariance of homology under barycentric subdivision](https://invisiblenetwork.ai/learn/nptel/111106905/deb3a11081af) (Video)
40. [Homotopy invariance of induced homomorphism](https://invisiblenetwork.ai/learn/nptel/111106905/b5ad627fe5f3) (Video)
41. [Finite vs Infinite simplicial complex](https://invisiblenetwork.ai/learn/nptel/111106905/93fc56a3f94d) (Video)
42. [Applications](https://invisiblenetwork.ai/learn/nptel/111106905/649d7eb8d4cf) (Video)
43. [Exact sequences](https://invisiblenetwork.ai/learn/nptel/111106905/4ed0acab6143) (Video)
44. [Zigzag Lemma](https://invisiblenetwork.ai/learn/nptel/111106905/c6740f05e188) (Video)
45. [Naturality](https://invisiblenetwork.ai/learn/nptel/111106905/504dae462643) (Video)
46. [Mayer-Vietoris Sequences](https://invisiblenetwork.ai/learn/nptel/111106905/4f6e008b7494) (Video)
47. [Excision](https://invisiblenetwork.ai/learn/nptel/111106905/c0324fea3eef) (Video)
48. [Local Homology](https://invisiblenetwork.ai/learn/nptel/111106905/7c72635a3085) (Video)
49. [Maps of spheres](https://invisiblenetwork.ai/learn/nptel/111106905/e30593bfeba3) (Video)
50. [Hopf trace theorem](https://invisiblenetwork.ai/learn/nptel/111106905/1be5144f0fd8) (Video)
51. [Hopf trace theorem & Euler number](https://invisiblenetwork.ai/learn/nptel/111106905/9f6e18ee68aa) (Video)
52. [Lefschetz fixed-point theorem](https://invisiblenetwork.ai/learn/nptel/111106905/ad54dafb98e8) (Video)
53. [Jordan curve theorem](https://invisiblenetwork.ai/learn/nptel/111106905/d317b952acc3) (Video)
54. [A glimpse of singular homology](https://invisiblenetwork.ai/learn/nptel/111106905/facc7c2a0056) (Video)
55. [Axioms for homology](https://invisiblenetwork.ai/learn/nptel/111106905/820b6f4b07c5) (Video)