Vol. 251, No. 1, 2011

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Chern numbers and the indices of some elliptic differential operators

Ping Li

Vol. 251 (2011), No. 1, 173–182

Libgober and Wood proved that the Chern number c1cn1 of a compact complex manifold of dimension n can be determined by its Hirzebruch χy-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 the result of Libgober and Wood, which was originally proved by induction.

Chern number, index, Dirac operator, signature operator
Mathematical Subject Classification 2000
Primary: 57R20
Secondary: 58J20
Received: 11 April 2010
Revised: 4 November 2010
Accepted: 27 November 2010
Published: 22 April 2011

Proposed: Kefeng Liu
Ping Li
Department of Mathematics
Tongji University
Shanghai, 200092