Alexander breadth bound on Seifert genus
= Alexander breadth bound on Seifert genus
{c}
{title2=$\operatorname{br}\Delta_K\leq2g_s(K)$}
A minimal-<genus> <Seifert surface> has a $2g_s(K)$-by-$2g_s(K)$ <Seifert matrix> $V$. Each entry of $tV-V^T$ has degree at most one, so its <determinant> has <breadth of a Laurent polynomial> at most $2g_s(K)$. This lower bound on <Seifert genus> need not be sharp: an untwisted <Whitehead double> can have <Alexander polynomial of a knot> $1$ and positive <Seifert genus>.