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Menasco, along with Morwen Thistlethwaite proved the Tait flyping conjecture, which states that given any two reduced alternating diagrams D1,D2 of an oriented, prime alternating link, D1 may be transformed to D2 by means of a sequence of certain simple moves called flypes.
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.