Ricci Flow with Surgery on Four-manifolds with Positive Isotropic Curvature
Differential Geometry
2007-05-23 v3
Abstract
In this paper we study the Ricci flow on compact four-manifolds with positive isotropic curvature and with no essential incompressible space form. Our purpose is two-fold. One is to give a complete proof of Hamilton's classification theorem on four-manifolds with positive isotropic curvature and with no essential incompressible space form; the other is to extend some recent results of Perelman on the three-dimensional Ricci flow to four-manifolds. During the the proof we have actually provided, up to slight modifications, all necessary details for the part from Section 1 to Section 5 of Perelman's second paper on the Ricci flow.
Keywords
Cite
@article{arxiv.math/0504478,
title = {Ricci Flow with Surgery on Four-manifolds with Positive Isotropic Curvature},
author = {Bing-Long Chen and Xi-Ping Zhu},
journal= {arXiv preprint arXiv:math/0504478},
year = {2007}
}
Comments
105 pages (revised)