Algebraic Topology · Problem 3.1.6

Cohomology — Allen Hatcher

Mathematics — Topology · simplicial-cohomology-surfaces

Problem

(a) Directly from the definitions, compute the simplicial cohomology groups of

S^1 \times S^1

with

\mathbb{Z}

and

\mathbb{Z}_2

coefficients, using the

\Delta

-complex structure given in §2.1. (b) Do the same for

\mathbb{RP}^2

and the Klein bottle.