منابع مشابه
Perelman Proves Poincaré
In 1904, Henri Poincaré conjectured: Every compact, connected, simply-connected 3-manifold is the 3-sphere. This conjecture has been near the center of a maelstrom of activity in topology, geometry, analysis, and many allied and sub-disciplines for a hundred years. Recently, Grisha Perelman announced a proof of the conjecture – in fact of the stronger Geometrization Conjecture of William Thurst...
متن کاملOn Perelman ’ S Papers
These are notes on Perelman’s papers “The Entropy Formula for the Ricci Flow and its Geometric Applications” [40] and “Ricci Flow with Surgery on Three-Manifolds’ [41]. In these two remarkable preprints, which were posted on the ArXiv in 2002 and 2003, Grisha Perelman announced a proof of the Poincaré Conjecture, and more generally Thurston’s Geometrization Conjecture, using the Ricci flow appr...
متن کاملEight Theses Reflecting on Stephen Toulmin
I discuss eight theses espoused or occasioned by Toulmin: (1) The validity standard is nearly always the wrong standard for real-life reasoning. (2) Little in good reasoning is topic neutral. (3) The probability calculus distorts much probabilistic reasoning. (4) Scant resources have a benign influence on human reasoning. (5) Theoretical progress and conceptual change are connected. (6) Logic s...
متن کاملThe Work of Grigory Perelman
Grigory Perelman has been awarded the Fields Medal for his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow. Perelman was born in 1966 and received his doctorate from St. Petersburg State University. He quickly became renowned for his work in Riemannian geometry and Alexandrov geometry, the latter being a form of Riemannian g...
متن کاملPerelman, Poincaré, and the Ricci Flow
In this expository article, we introduce the topological ideas and context central to the Poincaré Conjecture. Our account is intended for a general audience, providing intuitive definitions and spatial intuition whenever possible. We define surfaces and their natural generalizations, manifolds. We then discuss the classification of surfaces as it relates to the Poincaré and Thurston Geometriza...
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ژورنال
عنوان ژورنال: Hermès
سال: 1995
ISSN: 0767-9513,1963-1006
DOI: 10.4267/2042/15163