Ricci Flow on Open 4-Manifolds with Positive Isotropic Curvature |
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Authors: | Hong Huang |
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Affiliation: | 1. School of Mathematical Sciences, Key Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing, 100875, P.R. China
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Abstract: | In this note we prove the following result: Let X be a complete, connected 4-manifold with uniformly positive isotropic curvature, with bounded geometry, and with no essential incompressible space form. Then X is diffeomorphic to $mathbb{S}^{4}$ , or $mathbb{RP}^{4}$ , or $mathbb{S}^{3}timesmathbb {S}^{1}$ , or $mathbb{S}^{3}widetilde{times} mathbb{S}^{1}$ , or a possibly infinite connected sum of them. This extends work of Hamilton and Chen–Zhu to the noncompact case. The proof uses Ricci flow with surgery on complete 4-manifolds, and is inspired by recent work of Bessières, Besson, and Maillot. |
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