{"query": "The Poincare conjecture", "count": 13, "results": [{"id": "card_question_poincare", "title": "The Poincare conjecture", "shelf": "millennium", "surface": "secular", "snippet": "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", "authority_tier": "reference", "source": "Clay Mathematics Institute, the Millennium Prize Problems (2000)", "readable": false, "generated": false}, {"id": "card_floor_millennium", "title": "The Millennium floor - seven open questions, and where they connect", "shelf": "codex", "surface": "secular", "snippet": "The seven Millennium Prize Problems on the one map of reality. The FLOOR is what is proven or observed: the joints where two of the questions meet at one established thing - the GUE statistics shared ", "authority_tier": "engine_derived", "source": "Narrow Highway - the Millennium floor (operator seed)", "readable": false, "generated": false}, {"id": "card_spine_millennium_sources", "title": "The Millennium sources — the papers behind the seven sticks", "shelf": "spine", "surface": "secular", "snippet": "63 sources located for the seven Millennium sticks (Riemann, Birch and Swinnerton-Dyer, Navier-Stokes, Yang-Mills, P versus NP, Hodge, Poincare), one reference card each: the bibliographic record, DOI", "authority_tier": "reference", "source": "The Millennium sources — a spine of located records", "readable": false, "generated": false}, {"id": "card_src_mill_bochner_1946", "title": "S. Bochner 1946 — Vector fields and Ricci curvature", "shelf": "millennium", "surface": "secular", "snippet": "S. Bochner (1946). Vector fields and Ricci curvature. Bull. Amer. Math. Soc. 52 (1946) 776–797. DOI 10.1090/S0002-9904-1946-08647-4. Canonical: https://doi.org/10.1090/S0002-9904-1946-08647-4. Free co", "authority_tier": "reference", "source": "S. Bochner (1946), Bull. Amer. Math. Soc. 52 (1946) 776–797", "readable": false, "generated": false}, {"id": "card_src_mill_cao_zhu_2006", "title": "H.-D. Cao 2006 — A complete proof of the Poincaré and geometrization conjectures — application of the Hamilton-Perelman theory of the Ricci flow", "shelf": "millennium", "surface": "secular", "snippet": "H.-D. Cao, X.-P. Zhu (2006). A complete proof of the Poincaré and geometrization conjectures — application of the Hamilton-Perelman theory of the Ricci flow. Asian J. Math. 10 (2006) 165–492. DOI 10.4", "authority_tier": "reference", "source": "H.-D. Cao, X.-P. Zhu (2006), Asian J. Math. 10 (2006) 165–492", "readable": false, "generated": false}, {"id": "card_src_mill_morgan_tian_2007", "title": "J. Morgan 2007 — Ricci Flow and the Poincaré Conjecture", "shelf": "millennium", "surface": "secular", "snippet": "J. Morgan, G. Tian (2007). Ricci Flow and the Poincaré Conjecture. Clay Mathematics Monographs 3, AMS, 2007. arXiv: math/0607607. Canonical: https://bookstore.ams.org/CMIM/3. Free copy: https://arxiv.", "authority_tier": "reference", "source": "J. Morgan, G. Tian (2007), Clay Mathematics Monographs 3, AMS, 2007", "readable": false, "generated": false}, {"id": "card_src_mill_perelman_2003a", "title": "G. Perelman 2003 — Ricci flow with surgery on three-manifolds", "shelf": "millennium", "surface": "secular", "snippet": "G. Perelman (2003). Ricci flow with surgery on three-manifolds. arXiv (2003). arXiv: math/0303109. Canonical: https://arxiv.org/abs/math/0303109. Free copy: https://arxiv.org/abs/math/0303109. License", "authority_tier": "reference", "source": "G. Perelman (2003), arXiv (2003)", "readable": false, "generated": false}, {"id": "card_src_mill_kleiner_lott_2008", "title": "B. Kleiner 2008 — Notes on Perelman's papers", "shelf": "millennium", "surface": "secular", "snippet": "B. Kleiner, J. Lott (2008). Notes on Perelman's papers. Geom. Topol. 12 (2008) 2587–2855. DOI 10.2140/gt.2008.12.2587. arXiv: math/0605667. Canonical: https://doi.org/10.2140/gt.2008.12.2587. Free cop", "authority_tier": "reference", "source": "B. Kleiner, J. Lott (2008), Geom. Topol. 12 (2008) 2587–2855", "readable": false, "generated": false}, {"id": "card_src_mill_perelman_2002", "title": "G. Perelman 2002 — The entropy formula for the Ricci flow and its geometric applications", "shelf": "millennium", "surface": "secular", "snippet": "G. Perelman (2002). The entropy formula for the Ricci flow and its geometric applications. arXiv (2002). arXiv: math/0211159. Canonical: https://arxiv.org/abs/math/0211159. Free copy: https://arxiv.or", "authority_tier": "reference", "source": "G. Perelman (2002), arXiv (2002)", "readable": false, "generated": false}, {"id": "card_src_mill_perelman_2003b", "title": "G. Perelman 2003 — Finite extinction time for the solutions to the Ricci flow on certain three-manifolds", "shelf": "millennium", "surface": "secular", "snippet": "G. Perelman (2003). Finite extinction time for the solutions to the Ricci flow on certain three-manifolds. arXiv (2003). arXiv: math/0307245. Canonical: https://arxiv.org/abs/math/0307245. Free copy: ", "authority_tier": "reference", "source": "G. Perelman (2003), arXiv (2003)", "readable": false, "generated": false}, {"id": "card_src_mill_hamilton_1982", "title": "R. S. Hamilton 1982 — Three-manifolds with positive Ricci curvature", "shelf": "millennium", "surface": "secular", "snippet": "R. S. Hamilton (1982). Three-manifolds with positive Ricci curvature. J. Differential Geom. 17 (1982) 255–306. DOI 10.4310/jdg/1214436922. Canonical: https://doi.org/10.4310/jdg/1214436922. Free copy:", "authority_tier": "reference", "source": "R. S. Hamilton (1982), J. Differential Geom. 17 (1982) 255–306", "readable": false, "generated": false}, {"id": "card_floor_poincare", "title": "The Poincare chain - from the homology sphere and the heat flow to the closed question", "shelf": "codex", "surface": "secular", "snippet": "Two trees. Topology: Poincaré's homology sphere and the question (1904), Thurston's geometrization (1982). Geometric analysis: the heat-flow method of Eells and Sampson (1964), Hamilton's Ricci flow (", "authority_tier": "engine_derived", "source": "Narrow Highway - a chain on the one map (operator seed)", "readable": false, "generated": false}, {"id": "card_src_mill_arnold_1966", "title": "V. I. Arnold 1966 — Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits", "shelf": "millennium", "surface": "secular", "snippet": "V. I. Arnold (1966). Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits. Ann. Inst. Fourier 16 (1966) 319–361. DOI 10.5", "authority_tier": "reference", "source": "V. I. Arnold (1966), Ann. Inst. Fourier 16 (1966) 319–361", "readable": false, "generated": false}], "house": {"door": "FIND", "kind": "cards", "trail": "results", "seal": null, "next_step": {"do": "open the top card", "door": "FIND", "tool": "card_get", "params": {"id": "card_question_poincare"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}