Embeddable Knot

A Knot $K$ is an $n$-embeddable knot if it can be placed on a Genus $n$ standard embedded surface without crossings, but $K$ cannot be placed on any standardly embedded surface of lower Genus without crossings. Any Knot is an $n$-embeddable knot for some $n$. The Figure-of-Eight Knot is a 2-Embeddable Knot. A knot with Bridge Number $b$ is an $n$-embeddable knot where $n\leq b$.

See also Tunnel Number