TOPOLOGY-II Spring 2024
Lecture 1 -- Shapes, simplices, and singular n-chains
Lecture 2 -- Singular homology form a categorical point of view
Lecture 3 -- Functor, natural transformation, and homotopy
Lecture 4 -- Chain homotopy and homotopy invarience of singular homology
Lecture 5 -- Cross products and relative homology
Lecture 6 -- Long exact sequence of pairs
Lecture 7 -- Homology of spheres and Brower fixed point theorem
Lecture 8 -- Good pairs and relative homology
Lecture 9 -- Mayer Vietoris sequence
Lecture 10 -- Suspension isomorphism and reduced homology theory
Lecture 11 -- CW complex and CW homology
Lecture 12 -- Degree theory and the hairy ball theorem
Lecture 13 -- Degree of maps and calculation of CW homology
Lecture 14 -- Rings, modules, and tensor products
Lecture 15 -- Homology with coefficients
Lecture 16 -- Universal Coefficient theorem
Lecture 17 -- Cartesian products and CW-chain complexes
Lecture 18 -- Eilenberg-Zilber and Kunneth theorem
Lecture 19 -- Active learning component (Eulerian sketchbook)
Lecture 20 -- Applications of Kunneth theorem
Lecture 21 -- Cochain complex and cohomology theory
Lecture 22 -- Universal coefficient theorem for cohomlogy theory
Lecture 23 -- Cup product on singular cochains
Lecture 24 -- Orientation theory
Lecture 25 -- Poincare duality and calculation of cohomology rings
