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The Poincare conjecture
A question
The Poincare conjecture. Every simply connected closed three-manifold is homeomorphic to the three-sphere. Its chart is the tick stick stick_poincare_conjecture: what is sealed, what is cited and what stays open are read live at /stick?id=stick_poincare_conjecture. PROVEN by Grigori Perelman (2002-2003) by Hamilton's Ricci flow with surgery; the prize awarded in 2010 and declined.
source
card id
card_question_poincare
address
SCI.millennium.FCT/the-poincare-conjecture/REF.WITNESSED@clay-mathematics-institu
adjoining cards
- on the shelf of → The Millennium sources — the papers behind the seven sticks — one of the seven questions the Millennium shelf is about
- open end of → The Millennium floor - seven open questions, and where they connect — an open question hanging off the floor of what is proven
- connects at → Positive Ricci curvature kills harmonic one-forms — Positive Ricci curvature kills harmonic one-forms. bochner 1946; myers 1941; hamilton 1982
- connects at → Euler flow is geodesic flow on the volume-preserving diffeomorphisms — Euler flow is geodesic flow on the volume-preserving diffeomorphisms. arnold 1966. Cited,
- open end of → The logarithm - the instrument the joints share — the open question this chain reaches
- connects at → G. Perelman 2002 — The entropy formula for the Ricci flow and its geometric applications — where the logarithm enters: the entropy formula: Perelman's W functional is a log-Sobolev
- builds on → B. Kleiner 2008 — Notes on Perelman's papers — a later work standing on an earlier one
- builds on → H.-D. Cao 2006 — A complete proof of the Poincaré and geometrization conjectures — application of the Hamilton-Perelman theory of the Ricci flow — a later work standing on an earlier one
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