= Manin symbol
{c}
{title2=$[g]=\{g0,g\infty\}$}
For a finite-index modular subgroup, a Manin symbol records a coset and its associated oriented unimodular edge. Over the rationals the presentation has the relations $[g]+[gS]=0$ and $[g]+[gST]+[g(ST)^2]=0$, for inversion $S$ and translation $T$. They express reversing an edge and the boundary of a triangle. Integral computation also removes torsion caused by elliptic stabilizers. The boundary map sends the symbol to its terminal cusp minus its initial cusp; its kernel is absolute <homology>.
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