Hatcher-Algebraic-Topology · Problem 2B.11

Cohomology

Mathematics — Graph Theory · transfer-sequence-product-rp-infinity

Problem

Use the transfer sequence for the covering

X \times S^\infty \to X \times \mathbb{R}P^\infty

to produce isomorphisms

H_n(X \times \mathbb{R}P^\infty; \mathbb{Z}_2) \approx \bigoplus_{i \leq n} H_i(X; \mathbb{Z}_2)

for all

n