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Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)

 

 

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

DOI: https://doi.org/10.1090/S0894-0347-1990-1017783-4
Keywords: Sheaves and cohomology of sections of holomorphic vector bundles, characteristic classes and numbers
Article copyright: © Copyright 1990 American Mathematical Society