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Andy Putman
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Aside from the Geometrization Theorem/Poincare conjecture, probably the deepest theorem in low-dimensional topology in the last 10 years is the classification of hyperbolic structures on 3-manifolds with finitely generated fundamental group. Aside from the topological type, it turns out they they are classified by certain invariants "at infinity" (either Riemann surfaces at infinity or so-called "ending laminations"). The proof of this uses work of an enormous number of people : Agol, Alhfors, Bers, Brock, Calegari, Canary, Gabai, Namazi, Kleineidam, Kra, Lecuire, Marden, Maskit, Masur, Minsky, Mostow, Ohshika, Prasad, Rees, Souto, Sullivan, Thurston, and probably people I'm forgetting.

Andy Putman
  • 44.8k
  • 14
  • 186
  • 272