Homological Algebra: Basics and Applications

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Related lectures (32)

Page 3 of 4

Homology of Projective Space

Covers the homology of projective space, focusing on cohomology and exact sequences.

Universal Coefficient Theorems

Delves into the universal coefficient theorems in homological algebra, showcasing their practical application in computing homology and cohomology groups.

Graded Ring Structure on Cohomology

Explores the associative and commutative properties of the cup product in cohomology, with a focus on graded structures.

Decomposition of Group Algebras

Covers examples of group algebra decomposition and simple infinite-dimensional algebras.

Topology: Free Groups and Their Properties

Discusses the theory of free groups, their properties, and relationships with other algebraic structures.

Cross Product in Cohomology

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

Ample Invertible Sheaves

Introduces ample invertible sheaves and their properties in algebraic geometry.

Ideals and Representations

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Cohomology of C2: Cup Product

Covers the cup product in the cohomology of C2, showing how non-trivial elements are represented by cocycles.

Algebraic Geometry: Forms and Maps

Covers the concept of forms in algebraic geometry and the implications of constructing Bloch(A) from glued copies of A.