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Alternating knot
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==Hyperbolic volume== [[William Menasco|Menasco]], applying [[William Thurston|Thurston]]'s [[hyperbolization theorem]] for [[Haken manifold]]s, showed that any prime, non-split alternating link is [[hyperbolic link|hyperbolic]], i.e. the link complement has a [[hyperbolic geometry]], unless the link is a [[torus link]]. Thus hyperbolic volume is an invariant of many alternating links. [[Marc Lackenby]] has shown that the volume has upper and lower linear bounds as functions of the number of ''twist regions'' of a reduced, alternating diagram.
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