Related lectures (19)
Zig Zag Lemma
Covers the Zig Zag Lemma and the long exact sequence of relative homology.
Hurewicz Theorem
Explores the proof of the Hurewicz Theorem and its applications to spheres and homotopy groups.
Excision: An Example
Covers the concept of excision in algebraic topology with a focus on simplicial and singular homology.
Homology of Riemann Surfaces
Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.
Fundamental Groups
Explores fundamental groups, homotopy classes, and coverings in connected manifolds.
Relative Homotopy Groups
Covers relative homotopy groups, establishing long exact sequences and defining boundary homomorphisms.
Naturality: Chain Complexes and Homology Groups
Explores naturality in chain complexes, homology groups, and abelian groups, emphasizing the commutativity of squares and the Five-Lemma.
Cellular Approximation: Homotopy and CW Complexes
Explores the cellular approximation theorem for CW complexes and its implications on homotopy groups.
CW Approximation Uniqueness
Explores the uniqueness of CW approximation and Whitehead's theorem through the construction of maps inducing isomorphisms on homotopic groups.
Mayer-Vietoris Sequence
Explores the Mayer-Vietoris sequence, exact homomorphisms, embedded spheres, and path-connected spaces.

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