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arXiv · 1504.03078

A characterization of the $\hat{A}$-genus as a linear combination of Pontrjagin numbers

Ping Li
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Abstract

We show in this short note that if a rational linear combination of Pontrjagin numbers vanishes on all simply-connected $4k$-dimensional closed connected and oriented spin manifolds admitting a Riemannian metric whose Ricci curvature is nonnegative and nonzero at any point, then this linear combination must be a multiple of the $\hat{A}$-genus, which improves on a result of Gromov and Lawson. Our proof combines an idea of Atiyah and Hirzebruch and the celebrated Calabi-Yau theorem.

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Ping Li. 2015-04-13. A characterization of the $\hat{A}$-genus as a linear combination of Pontrjagin numbers. https://doi.org/10.1007/s00013-015-0842-6

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