Simply connected spin manifolds with positive scalar curvature

Miyazaki, Tetsuro

doi:10.1090/S0002-9939-1985-0776211-4

Simply connected spin manifolds with positive scalar curvature
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by Tetsuro Miyazaki PDF

Proc. Amer. Math. Soc. 93 (1985), 730-734 Request permission

Abstract:

Let ${l_n}$ be equal to 2 or 4 according as $n$ is congruent $\mod 8$ to zero or not. If the $\hat A$-genus of a compact simply connected spin manifold of dimension $n \geqslant 5$ vanishes, then the connected sum of ${l_n}$ copies of the manifold admits a metric of positive scalar curvature. This supports a conjecture of Gromov and Lawson.

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