Homology and Homotopy

Related lectures (31)

Page 3 of 4

Focuses on lifting properties in homotopy theory of chain complexes.

Explores the proof of the Hurewicz Theorem and its applications to spheres and homotopy groups.

Explores homotopy invariance and its application to homology groups of quotients, showcasing isomorphism and chain homotopy.

Covers the cup product on cohomology, acyclic models, and the universal coefficient theorem.

Outlines the proof of the excision theory using the barycentric subdivision.

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

Covers the long exact sequence of relative homology groups and chain complexes.

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

Covers the Postnikov tower, homotopy fibers, suspension, and the James construction.

Introduces reduced homology groups and explains their properties and applications in topology.