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

See also

Embedded Surface, Tunnel Number

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Cite this as:

Weisstein, Eric W. "Embeddable Knot." From MathWorld--A Wolfram Web Resource.

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