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

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

2005-04-23

arxiv.org/abs/math/0504478v3

Mathematics

Differential Geometry

105 pages (revised)

Scientific paper

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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