Ricci Flow with Surgery on Four-manifolds with Positive Isotropic Curvature

Bing-Long Chen; Xi-Ping Zhu

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Ricci Flow with Surgery on Four-manifolds with Positive Isotropic Curvature

Bing-Long Chen·Xi-Ping Zhu

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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.

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BibTeX RIS

Bing-Long Chen, Xi-Ping Zhu. 2006-06-04. Ricci Flow with Surgery on Four-manifolds with Positive Isotropic Curvature. https://arxiv.org/abs/math/0504478

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