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Course11110114465 lectures

Introduction to Algebraic Topology (Part-I)

Prof. Anant R. Shastri · IIT Bombay

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. Lecture 1 : Basic Problem in Topology Video
  2. Lecture 2 : Concept of homotopy Video
  3. Lecture 3 : Bird's eye-view of the course Video
  4. Lecture 4 : Path Homotopy Video
  5. Lecture 5 : Composition of paths Video
  6. Lecture 6 : Fundamental group π1 Video

Week 2

  1. Lecture 7 : Computation of Fund. Group of a circle Video
  2. Lecture 8 : Computation continued Video
  3. Lecture 9 : Computation concluded Video
  4. Lecture 10 : Van-Kampen's Theorem Video
  5. Lecture 11 : Function Spaces Video
  6. Lecture 12 : Quotient Maps Video

Week 3

  1. Lecture 13 : Group Actions Video
  2. Lecture 14 : Examples of Group Actions Video
  3. Lecture 15 : Assorted Results on Quotient Spaces Video
  4. Lecture 16 : Quotient Constructions Typical to Alg. Top. Video
  5. Lecture 17 : Quotient Constructions continued Video

Week 4

  1. Lecture 18 : Relative Homotopy Video
  2. Lecture 19 : Construction of a typical SDR Video
  3. Lecture 20 : Generalized construction of SDRs Video
  4. Lecture 21 : A theoretical application Video
  5. Lecture 22 : The Harvest Video

Week 5

  1. Lecture 23 : NDR pairs Video
  2. Lecture 24 : General Remarks Video
  3. Lecture 25 : Basics A ne Geometry Video
  4. Lecture 26 : Abstract Simplicial Complex Video
  5. Lecture 27 : Geometric Realization Video

Week 6

  1. Lecture 28 : Topology on |K| Video
  2. Lecture 29 : Simplical maps Video
  3. Lecture 30 : Polyhedrons Video
  4. Lecture 31 : Point Set topological Aspects Video
  5. Lecture 32 : Barycentric Subdivision Video

Week 7

  1. Lecture 33 : Finer Subdivisions Video
  2. Lecture 34 : Simplical Approximation Video
  3. Lecture 35 : Sperner Lemma Video
  4. Lecture 36 : Invariance of domain Video
  5. Lecture 37 : Proof of controled homotopy Video

Week 8

  1. Lecture 38 : Links and Stars Video
  2. Lecture 39 : Homotopical Aspects of Simplicial Complexes Video
  3. Lecture 40 : Homotopical Aspects Video
  4. Lecture 41 : Covering Spaces and Fund. Groups Video
  5. Lecture 42 : Lifting Properties Video

Week 9

  1. Lecture 43 : Homotopy Lifting Video
  2. Lecture 44 : Relation with the fund. Group Video
  3. Lecture 45 : Regular covering Video
  4. Lecture 46 : Lifting Problem Video
  5. Lecture 47 : Classification of Coverings Video

Week 10

  1. Lecture 48 : Classification Video
  2. Lecture 49 : Existence of Simply connected coverings Video
  3. Lecture 50 : Construction of Simply connected covering Video
  4. Lecture 51 : Properties Shared by total space and base Video
  5. Lecture 52 : Examples Video

Week 11

  1. Lecture 53 : G-coverings Video
  2. Lecture 54 : Pull-backs Video
  3. Week 11 : Lecture 55 Video
  4. Lecture 56 : Proof of classification Video
  5. Lecture 57 : Pushouts and Free products Video

Week 12

  1. Lecture 58 : Existence of Free Products, pushouts Video
  2. Lecture 59 : Free Products and free groups Video
  3. Lecture 60 : Seifert-Van Kampen Theorems Video
  4. Lecture 61 : Applications Video
  5. Lecture 62 : Applications continued Video

Live Session

  1. Live Session 05-02-2021 Video
  2. Live Session 24-02-2021 Video
  3. Live Session 19-03-2021 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
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