Homotopies & Equivalence Relations

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Related lectures (32)

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Fundamental Groups

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

Left Homotopy as an Equivalence Relation: The Homotopy Relation in a Model Category

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

Cell Attachment: Large Cell

Delves into cell attachment, exploring its implications for different cell dimensions.

Telescope Construction

Covers the construction of a telescope using cylinders on circles and the calculation of fundamental groups for various spaces.

Path Lifting

Explores path lifting, homotopy properties, and homomorphisms in covering spaces.

Retracte: Fundamental Group and Cell Attachment

Covers the concept of a subspace being a retract of another space and fundamental groups, including examples like contracting the teeth of a necklace.

Topology: Fundamental Groups and Surfaces

Discusses fundamental groups, surfaces, and their topological properties in detail.

The Topological Künneth Theorem

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

Topology: Homotopy and Cone Attachments

Discusses homotopy and cone attachments in topology, emphasizing their significance in understanding connected components and fundamental groups.

Chain Homotopy and Projective Complexes

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