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Lecture# Graded Ring Structure on Cohomology

Description

This lecture discusses the graded ring structure on cohomology, focusing on the associativity and commutativity of the cup product. The instructor explains the proof of the associative property and the graded commutativity, emphasizing the use of free ZG-resolution. The lecture concludes with the application of these concepts in the context of H*(Q8; Z), showcasing a class and an isomorphism for isomorphic morphisms.

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In course

MATH-506: Topology IV.b - cohomology rings

Singular cohomology is defined by dualizing the singular chain complex for spaces. We will study its basic properties, see how it acquires a multiplicative structure and becomes a graded commutative a

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Related concepts (381)

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