Fundamental groups of moebius strip and cylinder

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Reference no: EM13124329

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.

Reference no: EM13124329

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