Acyclic Models: Cup Product and Cohomology

Related lectures (32)

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

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

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

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

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

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

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.

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

Explores the homotopy theory of chain complexes over a field, focusing on closure properties and decomposition.