Eilenberg-Steenrod Axioms

Related lectures (32)

Page 3 of 4

Explores the CW Approximation Theorem, constructing CW complexes from spaces to ensure isomorphism on homology groups.

Covers spaces, homology, chain groups, and abelianization in CW complexes and maps.

Explores simplicial and singular homology, reduced homology groups, and their connection to the fundamental group.

Introduces homology as a tool to distinguish spaces in all dimensions and provides insights into its construction and applications.

Explores the long exact sequence of Ext-modules and their computations in homological algebra.

Covers induced homomorphisms, homotopy invariance, and homology groups of quotients.

Explores the homotopy theory of chain complexes, including path object construction and fibrations.

Covers the structure of topological spaces with A-complexes and chain complexes.

Introduces the concept of homology groups and focuses on a lemma about free abelian groups.

Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.