Miyazaki, Tetsuro On the existence of positive scalar curvature metrics on non-simply- connected manifolds. (English) Zbl 0541.53034 J. Fac. Sci., Univ. Tokyo, Sect. I A 30, 549-561 (1984). The author shows that the property that a spin (resp. orientable) manifold of dimension greater than four whose fundamental group is G admits a metric of positive scalar curvature depends only on its G-spin (resp. oriented) cobordism class. Then the author examines the case when G is a cyclic group of odd order or order two, a free group, or a direct sum of infinite cyclic groups. The method is based on that of M. Gromov and H. B. Lawson applied to simply connected manifolds [see Ann. Math., II. Ser. 111, 423-434 (1980; Zbl 0463.53025)]. Cited in 8 Documents MSC: 53C20 Global Riemannian geometry, including pinching 57R75 \(\mathrm{O}\)- and \(\mathrm{SO}\)-cobordism Keywords:G-cobordism; spin manifold; fundamental group; positive scalar curvature Citations:Zbl 0463.53025 PDFBibTeX XMLCite \textit{T. Miyazaki}, J. Fac. Sci., Univ. Tokyo, Sect. I A 30, 549--561 (1984; Zbl 0541.53034)