Homotopy groups of spheres

Related lectures (32)

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Explores the left homotopy relation as an equivalence relation in model categories.

Explores the construction of cylinder objects in chain complexes over a field, focusing on left homotopy and interval chain complexes.

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

Explores the homotopy theory of chain complexes over a field, focusing on closure properties and decomposition.

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

Covers cylinders, path objects, and homotopy in model categories.

Explores homotopy equivalence in chain complexes, emphasizing path object construction and left/right homotopy characterization.

Covers the attachment of a 2-cell to a space and explores the concept of the attachment application f.

Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.

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