Homotopy Invariance

Related lectures (31)

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Discusses the classification of surfaces and their fundamental groups using the Seifert-van Kampen theorem and polygonal presentations.

Introduces the homotopy category of a model category with inverted weak equivalences and unique homotopy equivalences.

Explores the homotopy extension property for contractable subspaces and their quotient maps.

Explores the Whitehead Lemma, showing when a morphism is a weak equivalence.

Discusses Laplace and Fourier transformations, focusing on their inversion formulas and applications in solving differential equations.

Covers the properties and structures of model categories, focusing on factorizations, model structures, and homotopy of continuous maps.

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Covers relative homotopy groups, establishing long exact sequences and defining boundary homomorphisms.

Explores the Serre model structure, focusing on left and right homotopy equivalences.

Explores chain homotopy, projective complexes, and homotopy equivalences in chain complexes.