Acyclic Models: Cup Product and Cohomology

This lecture covers the definition of the cup product on cohomology, the Künneth formula, and the universal coefficient theorem. It explains the concept of acyclic models, the cup product in cohomology, and the comparison of cellule cohomology with singular cohomology. The lecture also delves into the recollections about cohomology, the construction of chain complexes, and the universal coefficient theorem. The instructor discusses the singular cochain complex, the homomorphism between singular and cochain complexes, and the choice of basis for singular cochains.