Homotopies & Equivalence Relations

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Related lectures (34)

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.

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.

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.

Serre model structure: Left and right homotopy

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

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.

Homotopy Classes

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

Serre model structure on Top

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

Homotopy Theory: Cylinders and Path Objects

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

Attachment of a 2-cell

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

Symmetry: Noether Theorem

Explores the consequences of symmetry, focusing on the Noether Theorem and coordinated charges in Lie groups.

Higher Homotopy Groups: Generalization and Structure

Explores the generalization and structure of higher homotopy groups, including their abelianness, historical context, and properties of H spaces.

Sets of Left Homotopy Classes: The Homotopy Relation in a Model Category

Explores sets of left homotopy equivalence classes of morphisms in model categories.

Homotopy: Fundamentals and Examples

Covers the fundamentals of homotopy and its applications in topology.

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