Thurston's hyperbolization conjecture for closed 3-manifolds

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Let MM be a closed, orientable, atoroidal 3-manifold, meaning that it contains no essential torus. Thurston's hyperbolization conjecture. If MM has infinite fundamental group, then MM 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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