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arXiv · 1004.2142

Chern numbers and the indices of some elliptic differential operators

Ping Li
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Abstract

Libgober and Wood proved that the Chern number $c_{1}c_{n-1}$ of a $n$-dimensional compact complex manifold can be determined by its Hirzebruch $\chi_{y}$-genus. Inspired by the idea of their proof, we show that, for compact, spin, almost-complex manifolds, more Chern numbers can be determined by the indices of some twisted Dirac and signature operators. As a byproduct, we get a divisibility result of certain characteristic number for such manifolds. Using our method, we give a direct proof of Libgober-Wood's result, which was originally proved by induction.

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Ping Li. 2010-04-13. Chern numbers and the indices of some elliptic differential operators. https://doi.org/10.2140/pjm.2011.251.173

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