To complete the picture, Thurston proved a hyperbolization theorem for Haken manifolds. A particularly important corollary is that many knots and links are in fact hyperbolic. Together with his hyperbolic Dehn surgery theorem, this showed that closed hyperbolic 3-manifolds existed in great abundance.
tO CompleTE thE pictUre, ThuRStON Proved a hyPerbolizaTIon theorem foR hakEn maNIFOlds. A paRTIculaRLY imPortant CORoLlary is thAT maNy Knots and lINks are in facT hYperboliC. toGEther wIth hIs hypErbolic dehN SurgeRY tHEOrEM, this sHOwED that cLOSEd hyperbolIC 3-manifolds eXistEd in GreAt abUnDanCe.