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Course11110690555 lectures

Introduction to Algebraic Topology

Prof. Arpan Kabiraj · IIT Palakkad

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. Basics of Topology Video
  2. Some Topological Constructions and Homotopy Video
  3. Retraction and Deformation Retraction Video
  4. Contractible Spaces and Null Homotopy Video
  5. Some Questions Video

Week 2

  1. Simplicial Complex 1 Video
  2. Simplicial Complex 2 Video
  3. Simplicial Complex 3 Video
  4. Simplicial Complex 3 Delta Complex Video

Week 3

  1. Path Homotopy Video
  2. The Fundamental Group Video
  3. Covering Spaces Video
  4. Path Lifting Video
  5. Homotopy Lifting Video
  6. The Fundamental Group of a Circle Video

Week 4

  1. The Induced Homomorphism Video
  2. Applications Video
  3. The Fundamental Group of a Sphere Video
  4. Free Product of Groups Video
  5. Seifert–Van Kampen Theorem 1 Video
  6. Seifert–Van Kampen Theorem 2 Video

Week 5

  1. Lifting correspondence and Lifting criterion Video
  2. Classification of Covering Spaces 1 Video
  3. Classification of Covering Spaces 2 Video
  4. Classification of Covering Spaces 3 Video

Week 6

  1. The Group of Deck transformations Video
  2. Action of Deck Transformations Video
  3. Graphs and Free Groups Video

Week 7

  1. Free modules and chain complexes Video
  2. Notation and conventions Video
  3. The Simplicial Chain Complex Video
  4. Simplicial Homology : Examples Video
  5. Few results about Homology Video
  6. Relative Homology Video

Week 8

  1. Induced homomorphism 01 Video
  2. Induced homomorphism 02 Homology of a cone Video
  3. Induced homomorphism 03 Contiguous maps Video
  4. Induced homomorphism 04 Simplicial approximations and barycentric subdivisions Video
  5. Induced homomorphism 05 Invariance of homology under barycentric subdivision Video

Week 9

  1. Homotopy invariance of induced homomorphism Video
  2. Finite vs Infinite simplicial complex Video
  3. Applications Video
  4. Exact sequences Video
  5. Zigzag Lemma Video

Week 10

  1. Naturality Video
  2. Mayer-Vietoris Sequences Video
  3. Excision Video

Week 11

  1. Local Homology Video
  2. Maps of spheres Video
  3. Hopf trace theorem Video
  4. Hopf trace theorem & Euler number Video
  5. Lefschetz fixed-point theorem Video

Week 12

  1. Jordan curve theorem Video
  2. A glimpse of singular homology Video
  3. Axioms for homology Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Palakkad
Department
Mathematics
Teacher
Prof. Arpan Kabiraj
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. Coordinated by IIT Madras.
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