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Koszul complexes, harmonic oscillators, and the Todd class

Author: Jean-Michel Bismut
Journal: J. Amer. Math. Soc. 3 (1990), 159-256
MSC: Primary 58G12; Secondary 32L10, 57R20, 58G05, 58G11
MathSciNet review: 1017783
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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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Keywords: Sheaves and cohomology of sections of holomorphic vector bundles, characteristic classes and numbers
Article copyright: © Copyright 1990 American Mathematical Society

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