Also called the Tait flyping conjecture. Given two reduced alternating projections of the same knot, they are equivalent on the sphere iff they are related by a series of flypes. The conjecture was proved by Menasco and Thistlethwaite (1991, 1993) using properties of the Jones polynomial. It allows all possible reduced alternating projections of a given alternating knot to be drawn.

# Flyping Conjecture

## See also

Alternating Knot, Flype, Reducible Crossing, Tait's Knot Conjectures## Explore with Wolfram|Alpha

## References

Adams, C. C.*The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots.*New York: W. H. Freeman, pp. 164-165, 1994.Hoste, J.; Thistlethwaite, M.; and Weeks, J. "The First Knots."

*Math. Intell.*

**20**, 33-48, Fall 1998.Menasco, W. and Thistlethwaite, M. "The Tait Flyping Conjecture."

*Bull. Amer. Math. Soc.*

**25**, 403-412, 1991.Menasco, W. and Thistlethwaite, M. "The Classification of Alternating Links."

*Ann. Math.*

**138**, 113-171, 1993.Stewart, I.

*The Problems of Mathematics, 2nd ed.*Oxford, England: Oxford University Press, pp. 284-285, 1987.

## Referenced on Wolfram|Alpha

Flyping Conjecture## Cite this as:

Weisstein, Eric W. "Flyping Conjecture."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/FlypingConjecture.html