Thurston's hyperbolization conjecture for closed 3-manifolds

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.

Sources & referencesView supporting material

Primary source

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

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