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 eight knot is a 2-embeddable knot. A knot with bridge number b is an n-embeddable knot where n<=b.

embedded surface | tunnel number