Algebraic Topology · Problem 3.1.10

Cohomology — Allen Hatcher

Mathematics — Topology · lens-space-cohomology

Problem

For the lens space

L_m(\ell_1, \cdots, \ell_n)

defined in Example 2.43, compute the cohomology groups using the cellular cochain complex and taking coefficients in

\mathbb{Z}

\mathbb{Q}

\mathbb{Z}_m

, and

\mathbb{Z}_p

for

p

prime. Verify that the answers agree with those given by the universal coefficient theorem.