Homotopy groups of spheres

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Related lectures (32)

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Homotopies & Equivalence Relations

Covers homotopies, fundamental group, and equivalence relations in applications.

Homotopy Classes and Group Structures

Explores wedges in pointed spaces, group structures, and the Echman-Hilton argument.

Universal Covering Construction

Introduces the concept of a universal covering construction with examples like Hawaiian rings.

Base B for the covering

Explores constructing a base B for a topology using homotopy classes and paths.

Quasi-Categories: Active Learning Session

Covers fibrant objects, lift of horns, and the adjunction between quasi-categories and Kan complexes, as well as the generalization of categories and Kan complexes.

Serre model structure on Top

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

The Topological Künneth Theorem

Explores the topological Künneth Theorem, emphasizing commutativity and homotopy equivalence in chain complexes.

Cohomology Representations: Lecture 14.1

Covers the concept of cohomology representations and the implications of reduced suspension operations on spaces.

Seifert van Kampen: strategy

Covers the Seifert van Kampen theorem, homotopy, and the repair of premie rectangles.

Cell Attachment and Homotopy

Explores cell attachment, homotopy, function existence, construction using universal property, and continuity.