Perelman, Poincare, and the Ricci Flow

Details Perelman, Poincare, and the Ricci Flow Perelman, Poincare, and the Ricci Flow

2008-03-02

arxiv.org/abs/0803.0150v1

Mathematics

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9 pages, 2 figures

Scientific paper

In this expository article, we introduce the topological ideas and context central to the Poincare 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 Poincare and Thurston Geometrization conjectures. Finally, we survey Perelman's results on Ricci flows with surgery.

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