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