Algebraic Topology · Problem 2B.11

Cohomology — Allen Hatcher

Mathematics — Topology · transfer-sequence-product-rp-infinity

Problem

Use the transfer sequence for the covering

X \times S^\infty \to X \times \mathbb{RP}^\infty

to produce isomorphisms

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

for all

n