Lectures related to Homotopy group

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.

Understanding Lifting Properties in Homotopy Theory

Focuses on lifting properties in homotopy theory of chain complexes.

Chain Homotopy and Projective Complexes

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

Cohomology Representations: Lecture 14.1

Covers the concept of cohomology representations and the implications of reduced suspension operations on spaces.

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.

Model Categories: Properties and Structures

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

Homotopies & Equivalence Relations

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

Homotopy Theory in Chain Complexes

Explores acyclic fibrations and cylinder objects in chain complexes.

The Whitehead Lemma: Homotopy Equivalence in Model Categories

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

Homotopy Theory of Chain Complexes

Explores the homotopy theory of chain complexes over a field, focusing on closure properties and decomposition.

Homotopy theory of chain complexes

Explores the homotopy theory of chain complexes, focusing on defining cylinder objects and left homotopy.

Algebraic Kunneth Theorem

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

Universal Covering Construction

Introduces the concept of a universal covering construction with examples like Hawaiian rings.

Fundamental Groups

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

Unifying left and right homotopy: The homotopy relation

Explores the equivalence of left and right homotopy for morphisms between bifibrant objects.

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.

Homology and Homotopy

Explores the comparison of long exact sequences for vibrations and the relationship between homotopy and homology groups.

Attachment of a 2-cell

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

Long Exact Sequence in Homotopy

Explores the long exact sequence in homotopy, emphasizing the importance of sets and groups in the sequence.