Learn · Introduction to Algebraic Topology
Lecture 32 of 55Week 7
Simplicial Homology : Examples
Prof. Arpan Kabiraj · IIT Palakkad
Credits and licence
- From
- Introduction to Algebraic Topology, IIT Palakkad (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Madras.
- Who can watch
- Tweens profiles and older. How courses are placed
All the lectures
- Basics of Topology
- Some Topological Constructions and Homotopy
- Retraction and Deformation Retraction
- Contractible Spaces and Null Homotopy
- Some Questions
- Simplicial Complex 1
- Simplicial Complex 2
- Simplicial Complex 3
- Simplicial Complex 3 Delta Complex
- Path Homotopy
- The Fundamental Group
- Covering Spaces
- Path Lifting
- Homotopy Lifting
- The Fundamental Group of a Circle
- The Induced Homomorphism
- Applications
- The Fundamental Group of a Sphere
- Free Product of Groups
- Seifert–Van Kampen Theorem 1
- Seifert–Van Kampen Theorem 2
- Lifting correspondence and Lifting criterion
- Classification of Covering Spaces 1
- Classification of Covering Spaces 2
- Classification of Covering Spaces 3
- The Group of Deck transformations
- Action of Deck Transformations
- Graphs and Free Groups
- Free modules and chain complexes
- Notation and conventions
- The Simplicial Chain Complex
- Simplicial Homology : Examples
- Few results about Homology
- Relative Homology
- Induced homomorphism 01
- Induced homomorphism 02 Homology of a cone
- Induced homomorphism 03 Contiguous maps
- Induced homomorphism 04 Simplicial approximations and barycentric subdivisions
- Induced homomorphism 05 Invariance of homology under barycentric subdivision
- Homotopy invariance of induced homomorphism
- Finite vs Infinite simplicial complex
- Applications
- Exact sequences
- Zigzag Lemma
- Naturality
- Mayer-Vietoris Sequences
- Excision
- Local Homology
- Maps of spheres
- Hopf trace theorem
- Hopf trace theorem & Euler number
- Lefschetz fixed-point theorem
- Jordan curve theorem
- A glimpse of singular homology
- Axioms for homology