Lectures related to Attachment of a 1-cell

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

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

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

Model Categories: Properties and Structures

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

Serre model structure: Left and right homotopy

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

Induced Homomorphisms on Relative Homology Groups

Covers induced homomorphisms on relative homology groups and their properties.

Cell Attachment and Homotopy

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

Cellular Approximation: Homotopy and CW Complexes

Explores the cellular approximation theorem for CW complexes and its implications on homotopy groups.

Chain Homotopy and Projective Complexes

Explores chain homotopy, projective complexes, and homotopy equivalences 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.

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.

The Whitehead Lemma: Homotopy Equivalence in Model Categories

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

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.

Elementary Properties of Model Categories

Covers the elementary properties of model categories, emphasizing the duality between fibrations and cofibrations.

Euler Characteristic: Surfaces and Homotopy

Explores the Euler characteristic of surfaces and homotopy properties.

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.

Green-Riemann Formula: Curvilinear Integrals

Covers the Green-Riemann formula, connectedness by arcs, parametrization of curves, and open simply connected domains in the Oxy plane.

Algebraic Kunneth Theorem

Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.

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.