Thurston's hyperbolization conjecture for closed 3-manifolds
Thurston's hyperbolization conjecture for closed 3-manifolds
Let be a closed, orientable, atoroidal 3-manifold, meaning that it contains no essential torus. Thurston's hyperbolization conjecture. If has infinite fundamental group, then admits a hyperbolic structure. This conjecture was proven by Grigori Perelman in 2003, building upon Richard Hamilton's work on the Ricci flow, so its status is solved.
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Primary source
Charalampos Charitos, “A new proof of the virtual Haken conjecture”, arXiv:2510.00617 (2025).
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