← Theoretical / proof-based

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In this program

Singular cohomology
Universal coefficient theorem (statement)
Cup product
Ring structure on cohomology
Poincaré duality for closed oriented manifolds
Künneth formula (introduction)
Introduction to spectral sequences (optional)

Cohomology and duality

Künneth formula (introduction)

Algebraic topology · Theoretical / proof-based

Topic

Künneth formula (introduction)

Practice by unit: Cohomology and duality

Graduate Algebraic Topology — scope drawn from open algebraic topology notes and typical US graduate algebraic topology syllabi.

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