A crossing in a knot diagram for which there exists a circle in the projection plane meeting the diagram transversely at that crossing,
but not meeting the diagram at any other point. Removable crossings can be removed
by twisting, and so cannot occur in a knot diagram
of minimal link crossing number. Reducible
crossings are also called nugatory crossings (Tait 1898, Hoste *et al. *1998)
or removable crossings.

# Reducible Crossing

## See also

Alternating Knot, Knot Diagram, Reduced Knot Diagram## Explore with Wolfram|Alpha

## References

Hoste, J.; Thistlethwaite, M.; and Weeks, J. "The First Knots."*Math. Intell.*

**20**, 33-48, Fall 1998.Tait, P. G. "On Knots I, II, and III."

*Scientific Papers, Vol. 1.*Cambridge, England: University Press, pp. 273-347, 1898.

## Referenced on Wolfram|Alpha

Reducible Crossing## Cite this as:

Weisstein, Eric W. "Reducible Crossing."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/ReducibleCrossing.html