Tait Conjectures - The Tait Conjectures

The Tait Conjectures

Tait conjectured that in certain circumstances, crossing number was a knot invariant, specifically:

Any reduced diagram of an alternating link has the fewest possible crossings.

In other words, the crossing number of a reduced, alternating link is an invariant of the knot. This conjecture was proven by Morwen Thistlethwaite, Louis Kauffman and K. Murasugi in 1987, using the Jones polynomial. Another one of his conjectures:

A reduced alternating link with zero writhe is achiral.

This conjecture was also proven by Morwen Thistlethwaite.