Lectures related to Algebraic Kunneth Theorem

Group Cohomology

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Acyclic Models: Cup Product and Cohomology

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

The Topological Künneth Theorem

Explores the topological Künneth Theorem, emphasizing commutativity and homotopy equivalence in chain complexes.

Cohomology: Cross Product

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

Bar Construction: Homology Groups and Classifying Space

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.

Homomorphisms and Projective Resolutions

Covers homomorphisms, projective modules, and resolutions in chain complexes.

Homotopy Theory of Chain Complexes

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

Zig Zag Lemma

Covers the Zig Zag Lemma and the long exact sequence of relative homology.

Cohomology Groups: Hopf Formula

Explores the Hopf formula in cohomology groups, emphasizing the 4-term exact sequence and its implications.

Cohomology: Recollection and Foliations

Covers cohomology, injective resolutions, and acyclic objects in an abelian category.

Naturality: Chain Complexes and Homology Groups

Explores naturality in chain complexes, homology groups, and abelian groups, emphasizing the commutativity of squares and the Five-Lemma.

Cross Product in Cohomology

Explores the cross product in cohomology, covering its properties and applications in homotopy.

Long Exact Sequence of Ext-Modules

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

Natural Transformations in Algebra

Explores natural transformations in algebra, defining functors and isomorphisms.

Simplicial and Singular Homology Equivalence

Demonstrates the equivalence between simplicial and singular homology, proving isomorphisms for finite s-complexes and discussing long exact sequences.

Understanding Lifting Properties in Homotopy Theory

Focuses on lifting properties in homotopy theory of chain complexes.

Cohomology Real Projective Space

Covers cohomology in real projective spaces, focusing on associative properties and algebraic structures.

Homological Algebra: Basics and Applications

Covers the basics of Homological algebra, focusing on Ext modules and their significance in modern mathematics.

Free Resolution of Modules

Covers free resolution of modules and projective modules in module theory.

Homotopy theory of chain complexes

Explores the homotopy theory of chain complexes, focusing on retractions and model category structures.