Koszul complexes, harmonic oscillators, and the Todd class

Bismut, Jean-Michel

doi:10.1090/S0894-0347-1990-1017783-4

Koszul complexes, harmonic oscillators, and the Todd class
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by Jean-Michel Bismut

J. Amer. Math. Soc. 3 (1990), 159-256

DOI: https://doi.org/10.1090/S0894-0347-1990-1017783-4

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Abstract:

In this paper, we construct secondary characteristic classes associated with a short exact sequence of holomorphic Hermitian vector bundles. These secondary invariants are generalized analytic torsion forms associated with a family of elliptic operators. They are calculated in terms of Bott-Chern forms and of a certain complicated characteristic class. In a joint calculation with C. Soulé, we relate this characteristic class to the arithmetic Todd genus of Gillet and Soulé.

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