Relative Homotopy Groups

Related lectures (31)

Page 3 of 4

Explores the homotopy theory of chain complexes, focusing on model categories, weak equivalences, and the retraction axiom.

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

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

Explains the construction of the homotopy category of a model category using cofibrant and fibrant replacement.

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

Covers the fundamentals of homotopy and its applications in topology.

Covers the quadratic linking degree in knot theory, exploring its definitions, properties, and significance in algebraic geometry.

Discusses homotopy, projective spaces, and the universal property of quotient spaces in topology.

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

Explores homotopy invariance, emphasizing the preservation of properties under continuous functions and their relationship with topological spaces.