Cohomology Real Projective Space

This lecture covers the concept of cohomology in real projective spaces, focusing on the up product, cup product, and commutative diagrams. The instructor explains the associative and distributive properties of the cup product, as well as the isomorphism with Z or F2 coefficients. The lecture delves into the relative cup product, graded commutative R algebra, and the compatibility between up and cross products. Various propositions and proofs are presented to demonstrate the algebraic structures and properties of cohomology in real projective spaces.