Math 2.0

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Introduction to Algebraic Topology 3BDFH0NZYW

URIm2://res/3BDFH0NZYW
Kindcourse
CreatorsArpan Kabiraj (instructor)
Date2026-09-04
Scopein

Expressions

e1: edition

Languageen
Date2026-09-04
Contents
  • part 1: Week 1
  • session 1: Basics of Topology
  • session 2: Some Topological Constructions and Homotopy
  • session 3: Retraction and Deformation Retraction
  • session 4: Contractible Spaces and Null Homotopy
  • session 5: Some Questions
  • part 2: Week 2
  • session 6: Simplicial Complex 1
  • session 7: Simplicial Complex 2
  • session 8: Simplicial Complex 3
  • session 9: Simplicial Complex 3 Delta Complex
  • part 3: Week 3
  • session 10: Path Homotopy
  • session 11: The Fundamental Group
  • session 12: Covering Spaces
  • session 13: Path Lifting
  • session 14: Homotopy Lifting
  • session 15: The Fundamental Group of a Circle
  • part 4: Week 4
  • session 16: The Induced Homomorphism
  • session 17: Applications
  • session 18: The Fundamental Group of a Sphere
  • session 19: Free Product of Groups
  • session 20: Seifert–Van Kampen Theorem 1
  • session 21: Seifert–Van Kampen Theorem 2
  • part 5: Week 5
  • session 22: Lifting correspondence and Lifting criterion
  • session 23: Classification of Covering Spaces 1
  • session 24: Classification of Covering Spaces 2
  • session 25: Classification of Covering Spaces 3
  • part 6: Week 6
  • session 26: The Group of Deck transformations
  • session 27: Action of Deck Transformations
  • session 28: Graphs and Free Groups
  • part 7: Week 7
  • session 29: Free modules and chain complexes
  • session 30: Notation and conventions
  • session 31: The Simplicial Chain Complex
  • session 32: Simplicial Homology : Examples
  • session 33: Few results about Homology
  • session 34: Relative Homology
  • part 8: Week 8
  • session 35: Induced homomorphism 01
  • session 36: Induced homomorphism 02 Homology of a cone
  • session 37: Induced homomorphism 03 Contiguous maps
  • session 38: Induced homomorphism 04 Simplicial approximations and barycentric subdivisions
  • session 39: Induced homomorphism 05 Invariance of homology under barycentric subdivision
  • part 9: Week 9
  • session 40: Homotopy invariance of induced homomorphism
  • session 41: Finite vs Infinite simplicial complex
  • session 42: Applications
  • session 43: Exact sequences
  • session 44: Zigzag Lemma
  • part 10: Week 10
  • session 45: Naturality
  • session 46: Mayer-Vietoris Sequences
  • session 47: Excision
  • part 11: Week 11
  • session 48: Local Homology
  • session 49: Maps of spheres
  • session 50: Hopf trace theorem
  • session 51: Hopf trace theorem & Euler number
  • session 52: Lefschetz fixed-point theorem
  • part 12: Week 12
  • session 53: Jordan curve theorem
  • session 54: A glimpse of singular homology
  • session 55: Axioms for homology

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