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Course11110115262 lectures

Introduction to Algebraic Topology (Part-II)

Prof. Anant R. Shastri · IIT Bombay

Start with lecture 1 At NPTEL

Lectures

week-01

  1. Week 1-Lecture 1 : Introduction Video
  2. Week 1-Lecture 2 : Attaching cells Video
  3. Week 1-Lecture 3 : Subcomplexes and Examples Video
  4. Week 1-Lecture 4A : More examples Video
  5. Week 1-Lecture 4B : More Examples Video
  6. Weeek 1-Lecture 5 : Topological Properties Video

week-02

  1. Week 2-Lecture 6 : Coinduced Topology Video
  2. Week 2-Lecture 7 : Compactly generated topology on Products Video
  3. Week 2-Lecture 8 : Product of Cell complexes Video
  4. Week 2-Lecture 9 : Product of Cell complexes-Continued Video
  5. Week 2-Lecture 10 : Partition of Unity on CW-complexes Video

week-03

  1. Week 3-Lecture 11 : Partition of Unity-Continued Video
  2. Week 3-Lecture 12 : Homotopical Aspects Video
  3. Week 3-Lecture 13 : Homotopical Aspects-Continued Video
  4. Week 3-Lecture 14 : Cellular Maps Video
  5. Week 3-Lecture 15 : Cellular Maps-Continued Video

week-04

  1. Week 4-Lecture 16A : Homotopy exact sequence of a pair Video
  2. Week 4-Lecture 16B : Homotopy exact sequence of a fibration Video
  3. Week 4-Lecture 17 : Categories-Definitions and Examples Video
  4. Week 4-Lecture 18 : More Examples Video
  5. Week 4-Lecture 19 : Functors Video
  6. Week 4-Lecture 20 : Equivalence of Functors-Continued Video

week-05

  1. Week 5-Lecture 21 : Universal Objects Video
  2. Week 5-Lecture 22 : Basic Homological Algebra Video
  3. Week 5-Lecture 23 : Diagram-Chasing Video
  4. Week 5-Lecture 24 : Homology of Chain Complexes Video
  5. Week 5-Lecture 25 : Euler Characteristics Video

week-06

  1. Week 6-Lecture 26 : Singular Homology Groups Video
  2. Week 6-Lecture 27 : Basic Properties of Singular Homology Video
  3. Week 6-Lecture 28 : Excision Video
  4. Week 6-Lecture 29 : Examples of Excision-Mayer Vietoris Video
  5. Week 6-Lecture 30 : Applications Video

week-07

  1. Week 7-Lecture 31 : Applications-Continued Video
  2. Week 7-Lecture 32 : The Singular Simplicial Homology Video
  3. Week 7-Lecture 33 : Simplicial Homology Video
  4. Week 7-Lecture 34 : Simplicial Homology-Continued Video
  5. Week 7-Lecture 35 : CW-Homology and Cellular Singular Homology Video

week-08

  1. Week 8-Lecture 36 : Construction of CW-chain complex Video
  2. Week 8-Lecture 37 : CW structure and CW homology of Lens Spaces Video
  3. Week 8-Lecture 38 : Assorted Topics Video
  4. Week 8-Lecture 39 : Some Applications of Homology Video
  5. Week 8-Lecture 40 : Applications of LFT Video

week-09

  1. Week 9-Lecture 41 : Jordan-Brouwer Video
  2. Week 9-Lecture 42 : Proof of Lemmas Video
  3. Week 9-Lecture 43 : Relation between ?1 and H1 Video
  4. Week 9-Lecture 44 : All Postponed Proofs Video
  5. Week 9-Lecture 45 : Proofs-Continued Video

week-10

  1. Week 10-Lecture 46 : Definitions and Examples Video
  2. Week 10-Lecture 47 : Paracompactness Video
  3. Week 10-Lecture 48 : Manifolds with Boundary Video
  4. Week 10-Lecture 49 : Embeddings and Homotopical Aspects Video
  5. Week 10-Lecture 50 : Homotopical Aspects continued Video

week-11

  1. Week 11-Lecture 51 : Classification of 1-manifolds Video
  2. Week 11-Lecture 52 : Classification of 1-manifolds-continued Video
  3. Week 11-Lecture 53 : Triangulation of Manifolds Video
  4. Week 11-Lecture 54 : Pseudo-Manifolds Video
  5. Week 11-Lecture 55 : One result due to Poincaŕe and another due to Munkres Video

week-12

  1. Week 12-Lecture 56 : Some General Remarks Video
  2. Week 12-Lecture 57 : Classification of Compact Surface Video
  3. Week 12-Lecture 58 : Final Reduction-Completion of the Proof Video
  4. Week 12-Lecture 59 : Proof of Part B Video
  5. Week 12-Lecture 60 : Orientability Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Bombay
Department
Mathematics
Teacher
Prof. Anant R. Shastri
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
Who can watch
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