# Poincaré conjecture

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## Poincaré conjecture

[‚pwän‚kä′rā kən‚jek·chər]
(mathematics)
The question as to whether a compact, simply connected three-dimensional manifold without boundary must be homeomorphic to the three-dimensional sphere.
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Perelman ([19], [20]) used Ricci flow and its surgery to prove Poincare conjecture. The Ricci flow is an evolution equation for metrics on a Riemannian manifold defined as follows:
Fermat's Last Theorem, The Poincare Conjecture, Isaac Newton and Einstein are just some of the fascinating stories and personalities the students have been able to explore with Jarad.
Clay Research Conference: Resolution of the Poincare Conjecture (2010: Paris, France) Edited by James Garlson
More recently, Grigory Perelman, a Russian, won the Fields Medal for his proof of the famous topological problem known as the Poincare Conjecture.
Sobolev inequalities, heat kernels under Ricci flow, and the Poincare conjecture.
Perelman, 43, said he believes his contribution in proving the Poincare conjecture was no greater than that of US mathematician Richard Hamilton, who first suggested a program for the solution.
The 44- year- old mathematician had solved the Poincare conjecture, which deals with shapes that exist in four or more dimensions rather than the familiar three.
Certain aspects of Perelman's work on the Poincare conjecture have applications in physics and we want to suggest a few formulas in this direction; a fuller exposition will appear in a book in preparation [8].
Petersburg solved the "Poincare Conjecture." His solution won Perelman math's highest honor, the Fields Medal, described as the mathematical equivalent of the Super Bowl.
The Clay outfit offers \$1 million for the solution to any of seven long-standing puzzles in mathematics, and the Poincare conjecture is one of them.
The Poincare Conjecture involves the study of shapes, spaces and surfaces and makes predictions about the topology of multi-dimensional objects.
Disguised spheres A Russian mathematician offered a proof of the Poincare conjecture, a question about the shapes of three-dimensional spaces, but it remained unclear whether the proof is solid (163: 259, 378 *).

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