Complete 4-manifolds with uniformly positive isotropic curvature

2009/12/30 by Huang, Hong
#53C44 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0912.5405

Abstract

We prove the following result: Let (X,g₀) be a complete, connected 4-manifold with uniformly positive isotropic curvature and with bounded geometry. Then there is a finite collection F of manifolds of the form \mathbbS³ × ℝ /G, where G is a fixed point free discrete subgroup of the isometry group of the standard metric on \mathbbS³× ℝ, such that X is diffeomorphic to a (possibly infinite) connected sum of copies of \mathbbS⁴,\mathbbRP⁴ and/or members of F. This extends recent work of Chen-Tang-Zhu and Huang. We also extend the above result to the case of orbifolds. The proof uses Ricci flow with surgery on complete orbifolds.

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