$\hat{A}$ -亏格是Pontrjagin数的线性组合的一个刻划
A characterization of the $\hat{A}$-genus as a linear combination of Pontrjagin numbers
摘要：
我们在这个简短的说明，如果一个合理的线性组合的Pontrjagin数消失在所有单连通$4k$维封闭连通和定向自旋流形承认黎曼度量的里奇曲率是非负和非零的任何一点，那么这个线性组合必须是一个倍数的$\hat{A}$ -genus，这改善了Gromov和Lawson的结果。我们的证明结合了Atiyah和Hirzebruch的思想和著名的Calabi-Yau定理。
英文摘要：
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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