Perelman, Poincare, and the Ricci Flow

2008/03/02 by Scott D. Kominers, Kominers, Scott D.
Mathematics · #53-01 #53A05 #57M40 #FOS: Mathematics #Geometric Topology (math.GT) #History and Overview (math.HO) #math.GT #math.HO #msc:53-01 #msc:53A05 #msc:57M40

paper · pdf · doi:10.48550/arxiv.0803.0150

9 pages, 2 figures

arxiv created 2008/03/02 · arxiv updated 2011/01/04

Abstract

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.

Related

• Ricci Flow and the Poincare Conjecture
• Ricci flow on Poincare' and Thurston's Geometrization Conjecture
• Hamilton-Perelman's Proof of the Poincaré Conjecture and the Geometrization Conjecture
• Completion of the Proof of the Geometrization Conjecture
• Perelman's proof of the Poincaré conjecture: a nonlinear PDE perspective