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 eight knot is a 2-embeddable knot. A knot with bridge number is an -embeddable knot where .

# Embeddable Knot

## See also

Embedded Surface, Tunnel Number## Explore with Wolfram|Alpha

## Cite this as:

Weisstein, Eric W. "Embeddable Knot."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/EmbeddableKnot.html