= Boundary loop of a once-punctured torus
{title2=$[a,b]=aba^{-1}b^{-1}$}
In the standard <free basis of a group> $a,b$ for the <fundamental group of a once-punctured torus>, its oriented <boundary loop> represents $aba^{-1}b^{-1}$ up to <orientation> and <conjugation>. The square model proves this: radial <deformation retraction> takes the inner boundary once around the four sides, whose orientations read $a,b,a^{-1},b^{-1}$. Attaching a <simply connected space> along that boundary kills the <normal closure> of the <commutator of group elements>, whenever the hypotheses of the <Seifert-van Kampen theorem> hold.
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