A characterization of the -genus as a linear combination of Pontrjagin numbers
arXiv:1504.03078 · doi:10.1007/s00013-015-0842-6
Abstract
We show in this short note that if a rational linear combination of Pontrjagin numbers vanishes on all simply-connected -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 -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.
5 pages