flyping conjecture - Wolfram|Alpha

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Input interpretation

flyping conjecture

Alternate name

Tait flyping conjecture

Definition

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.

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Related terms

alternating knot | flype | reducible crossing | Tait's knot conjectures

Subject classifications

MathWorld

general knot theory | solved problems

MSC 2010

57M25 | 57Q45

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