Algebraic Topology · Problem 16

Cohomology — Allen Hatcher

Mathematics — Topology · torsion-prime-power-product

Problem

Show that if

X

and

Y

are finite CW complexes such that

H^*(X; \mathbb{Z})

and

H^*(Y; \mathbb{Z})

contain no elements of order a power of a given prime

p

, then the same is true for

X \times Y

. [Apply Theorem 3.15 with coefficients in various fields.]