Ricci flow on open 4-manifolds with positive isotropic curvature

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 ${\mathbb{S}}^3\times {\mathbb{S}}^1$, or ${\mathbb{S}}^3\tilde{\times }{\mathbb{S}}^1$, 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 Bessi$\grave{e}$res, Besson and Maillot.

25 pages

References in corpus (3)

• Ricci flow on open 3-manifolds and positive scalar curvature
• Complete 4-manifolds with uniformly positive isotropic curvature
• Four-orbifolds with positive isotropic curvature

Cited by in corpus (1)

• Three-orbifolds with positive scalar curvature