Homotopies & Equivalence Relations

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Related lectures (32)

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Topology: Classification of Surfaces and Fundamental Groups

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

Homotopy Equivalence in Chain Complexes

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

Serre model structure: Left and right homotopy

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

Universal Covering

Explores the concept of a universal cover of a topological space and the necessary conditions for a space to have one.

The Whitehead Lemma: Homotopy Equivalence in Model Categories

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

Topology: Fundamental Groups and Applications

Provides an overview of fundamental groups in topology and their applications, focusing on the Seifert-van Kampen theorem and its implications for computing fundamental groups.

Model Categories: Properties and Structures

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

Homotopy Classes

Covers the concept of homotopy classes and their properties in topology, including short components and group concatenation.

Homotopy Theory in Care Complexes

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

Serre model structure on Top

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