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Related lectures (32)

Cohomology: Recollection and Foliations

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

Induced Homomorphisms

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

Algebra: Chain Complexes

Explores chain complexes, abelian groups, homomorphisms, homology groups, and free abelian groups.

EML Spaces and Cohomology

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

Cohomology: Cup Product

Covers the cup product in cohomology, focusing on examples and computations.

Cup and Cap Product: Poincaré Duality

Explains the cup and cap product in algebraic topology and their relation to homology groups.

Algebraic Kunneth Theorem

Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.

Isogeny Graphs: Eigenvalues and Cryptography

Explores isogeny graphs of supersingular elliptic curves, showing optimal mixing times for random walks and applications to cryptography.

Graded Ring Structure on Cohomology

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

Serre model structure on Top

Explores the Serre model structure on Top, focusing on right and left homotopy.

Symmetric Group: Cycle Notation

Explores the symmetric group, emphasizing cycle notation and group properties.

Injective Modules: Ox-Modules and Injectives

Covers injective modules, Ox-modules, and their relevance in algebraic structures, emphasizing their importance in resolving acyclic resolutions and computing cohomology.

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