Cup and Cap Product: Poincaré Duality

Related lectures (31)

Explores the concept of a commutative semi-ring based on set theory properties.

Explains relative homology, n-cycles, n-boundaries, and exact sequences of chain complexes.

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

Explores natural numbers, their properties, operations, and practical applications like calculating hours in a year.

Explores simplicial and singular homology, reduced homology groups, and their connection to the fundamental group.

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

Covers the concept of excision in algebraic topology with a focus on simplicial and singular homology.

Covers the long exact sequence of relative homology groups and chain complexes.

Covers the concept of orientation and degrees in topology, focusing on assigning orientations to manifolds.

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

Explains cellular homology and the computation of homology groups using boundary maps.

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