Lecture

Retracte: Fundamental Group and Cell Attachment

Related lectures (31)

Serre model structure on Top

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

Fundamental Groups

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

Homotopy Theory: Cylinders and Path Objects

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

Topology: Homotopy and Cone Attachments

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

Cell Attachment: Large Cell

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

Homotopies & Equivalence Relations

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

Serre model structure: Left and right homotopy

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

Attachment of a 2-cell

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

The Topological Künneth Theorem

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

CW Pairs: Homotopy Extension Property

Discusses how CW pairs satisfy the homotopy extension property through retractions and homotopy extension properties.

Model Categories: Properties and Structures

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

Bar Construction: Homology Groups and Classifying Space

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.

Topology: Disk Deprivation

Delves into disk deprivation in topology, showcasing how spaces emerge from this process.

Telescope Construction

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

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.

Cell Attachment and Homotopy

Covers cell attachment, homotopy, mappings, and universal properties in topology.

Homotopy Lifting Property

Explores the homotopy lifting property, demonstrating how to lift homotopic maps and solve lifting problems on different spaces.

Cell Attachment and Homotopy

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

Topology: Fundamental Groups and Surfaces

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

Chain Homotopy and Projective Complexes

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