= Seifert-matrix presentation of the Alexander module
{c}
{title2=$\mathcal A_K=\operatorname{coker}(tV-V^T)$}
Cut a <knot exterior> along a <Seifert surface> and stack copies to form its <infinite cyclic cover>. Linking-dual generators for the <homology> of the cut-open piece give the positive and negative inclusion <matrices> $V$ and $V^T$ in row convention. The gluing relations therefore have <matrix> $tV-V^T$. The H0 gluing map is multiplication by $t-1$ and is injective, so these relations present the entire <Alexander module of a knot>. Its order is the determinant, up to a Laurent unit.
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