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On the existence of positive scalar curvature metrics on non-simply- connected manifolds. (English) Zbl 0541.53034

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)].

MSC:

53C20 Global Riemannian geometry, including pinching
57R75 \(\mathrm{O}\)- and \(\mathrm{SO}\)-cobordism

Citations:

Zbl 0463.53025
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