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Hyperbolization theorem
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<p>In <a href="/facts/Geometry/wTQf5ffQ">geometry</a>, <a href="/facts/William_Thurston/K1Qe8801">Thurston's</a> geometrization theorem or hyperbolization theorem implies that closed atoroidal <a href="/facts/Haken_manifold/ebWXqIvC">Haken manifolds</a> are hyperbolic, and in particular satisfy the <a href="/facts/Thurston_conjecture/FDpqIM7y">Thurston conjecture</a>. </p>