Question:
Fundamental groups of the Moebius strip and the cylinder.
Show that the Mobius strip and the cylinder both have fundamental group Z.
We can use the following theorem:
If G acts on X, pi1(X) = {e}, and for all x elements of X there exists Ux neighborhood of X such that Ux intersection g(Ux) = empty set for all g elements of G{e}, then pi1(XG) is homeomorphic to G.