Four-orbifolds with positive isotropic curvature (Q265094)

Continuing previous work of the author [J. Geom. Anal. 23, No. 3, 1213--1235 (2013; Zbl 1273.53059)] on the classification of open 4-manifolds with uniformly positive isotropic curvature, the author shows that if \((X,g_0)\) is a complete, connected 4-manifold with uniformly positive isotropic curvature and with bounded geometry, then there is a finite collection \(\mathcal{F}\) of manifolds of the form \((\mathbb{S}^3\times\mathbb{R})/G\), where \(G\) is a discrete subgroup of the isometry group of the round cylinder \(\mathbb{S}^3\times\mathbb{R}\) on which \(G\) acts freely, such that \(X\) is diffeomorphic to a possibly infinite connected sum of \(\mathbb{S}^4,\mathbb{RP}^4\), and members of \(\mathcal{F}\). A result of \textit{M. J. Micallef} and \textit{M. Y. Wang} [Duke Math. J. 72, No.3, 649-672 (1993; Zbl 0804.53058), shows that the converse holds. This result also extends the main theorem of \textit{B-L. Chen, S-H. Tang}, and \textit{X-P. Zhu} [J. Differ. Geom. 91, No. 1, 41--80 (2012; Zbl 1257.53053)] to the noncompact case. The techniques used in the proof allow the author to generalize the manifold result to open 4-orbifolds as well.