= Boundary of a Möbius band winds twice around its core
{title2=$\deg(\partial M\to C)=2$}
In the <quotient space> description of the <Möbius band>, follow $v=+1$ once along the rectangle. The seam sends its endpoint to the start of $v=-1$, which must also be traversed before returning to the original point. Under the <deformation retraction> onto the <core circle of a Möbius band>, these two stretches each travel once around the same <circle>. Orienting both circles by increasing longitudinal parameter gives a map of <topological degree> two. Equivalently, the <group homomorphism> on <fundamental groups> induced by inclusion of the <boundary> sends a chosen generator to twice the core generator, or to $c^2$ in multiplicative notation. Reversing the chosen boundary generator changes the sign, not the fact that it winds twice.
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