Concept
Universal coefficient theorem
Related lectures (19)
Homology with coefficients
Covers homology with coefficients, introducing the concept of defining homology groups with respect to arbitrary abelian groups.
Universal Coefficient Theorems
Delves into the universal coefficient theorems in homological algebra, showcasing their practical application in computing homology and cohomology groups.
Acyclic Models: Cup Product and Cohomology
Covers the cup product on cohomology, acyclic models, and the universal coefficient theorem.
Cohomology Operations: Cup Products and Bockstein
Explores cup products, Bockstein homomorphisms, and Steenrod algebra in cohomology.
Cross Product in Cohomology
Explores the cross product in cohomology, covering its properties and applications in homotopy.
Homomorphisms and Projective Resolutions
Covers homomorphisms, projective modules, and resolutions in chain complexes.
Homology groups: Quotients
Covers homology groups of quotients, homotopy invariance, and exact sequences.
Graded Ring Structure on Cohomology
Explores the associative and commutative properties of the cup product in cohomology, with a focus on graded structures.
Steenrod Squares
Covers the concept of Steenrod Squares and their applications in stable cohomology operations.
Homological Algebra: Basics and Applications
Covers the basics of Homological algebra, focusing on Ext modules and their significance in modern mathematics.