The fundamental group of the Möbius strip What is the fundamental group of the Möbius strip?
Is it given by $\{-1,1\}$ as the lemma of Synge supposes, or am I wrong and it does not apply there?
The moebius strip is homotopy-equivalent to the circle, so has the same fundamental group which is $\mathbb Z$.
The fundamental group of the moebius strip is $\{a,b|a^2=b^2\}$.
Cf. http://www2.math.ou.edu/~forester/5863S14/fsol.pdf