Menasco, applying Thurston's hyperbolization theorem for Haken manifolds, showed that any prime, non-split alternating link is hyperbolic, i.e. the link complement has a hyperbolic geometry, unless the link is a torus link.
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Morwen Thistlethwaite, Louis Kauffman and K. Murasugi proved the first two Tait conjectures in 1987 and Morwen Thistlethwaite and William Menasco proved the Tait flyping conjecture in 1991.
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