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 NumberExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Embeddable Knot." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EmbeddableKnot.html