Manifolds Carrying Large Scalar Curvature
Bechtluft-Sachs, Stefan (1999) Manifolds Carrying Large Scalar Curvature. Asian Journal of Mathematics , 3 (2). pp. 373-380. ISSN 1093-6106
Let W = S E be a complex spinor bundle with vanishing first Chern class over a simply connected spin manifold M of dimension 5. Up to connected sums we prove that W admits a twisted Dirac operator with positive order-0-term in the Weitzenb¨ock decomposition if and only if the characteristic numbers Aˆ(TM)[M] and ch (E)Aˆ(TM)[M] vanish. This is achieved by generalizing  to twisted Dirac operators.
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