A characterization of the (A)over-cap-genus as a linear combination of Pontrjagin numbers

作者：Li, Ping^*

来源：ARCHIV DER MATHEMATIK, 2016, 106(1): 85-90.

DOI：10.1007/s00013-015-0842-6

• (A)over-cap-genus
• Spin manifold
• Ricci curvature
• Positive scalar curvature
• Pontrjagin number

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 not identically zero, then this linear combination must be a multiple of the (A) over cap -genus, which improves a result of Gromov and Lawson. Our proof combines an idea of Atiyah and Hirzebruch and the celebrated Calabi-Yau theorem.

• 出版日期2016-1
• 单位同济大学