Perelman, Poincare, and the Ricci Flow
History and Overview
2011-01-04 v1 Geometric Topology
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.
Keywords
Cite
@article{arxiv.0803.0150,
title = {Perelman, Poincare, and the Ricci Flow},
author = {Scott D. Kominers},
journal= {arXiv preprint arXiv:0803.0150},
year = {2011}
}
Comments
9 pages, 2 figures