Hatcher-Algebraic-Topology · Problem 3.1.6

Cohomology

Mathematics — Graph Theory · simplicial-cohomology-torus-rp2-klein

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{R}P^2

and the Klein bottle.