Bridge Number

The least number of unknotted arcs lying above the plane in any projection. The knot 05-002 has bridge number 2. Such knots are called 2-Bridge Knots. There is a one-to-one correspondence between 2-Bridge Knots and rational knots. The knot 08-010 is a 3-bridge knot. A knot with bridge number $b$ is an $n$-Embeddable Knot where $n\leq b$.

See also Bridge Index

References

Adams, C. C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. New York: W. H. Freeman, pp. 64-67, 1994.

Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, p. 115, 1976.