Let $L\colon S^1 \sqcup S^1 \dots S^1 \hookrightarrow S^3$ be a link. A Seifert surface for $L$ is an embedded, compact, oriented surface $i\colon \Sigma \hookrightarrow S^3$ such that it bounds the link, i.e. $\partial \Sigma = L$. Usually, $\Sigma$ is assumed to be connected.