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.
References
Primary source
Charalampos Charitos, “A new proof of the virtual Haken conjecture”, arXiv:2510.00617 (2025).
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