Hatcher-Algebraic-Topology · Problem 13

Cohomology

Mathematics — Graph Theory · cohomology-ring-cp-inf-quotient

Problem

Describe

H^*(\mathbb{C}P^\infty/\mathbb{C}P^1; \mathbb{Z})

as a ring with finitely many multiplicative generators. How does this ring compare with

H^*(S^6 \times \mathbb{H}P^\infty; \mathbb{Z})