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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

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

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Koszul complexes, harmonic oscillators, and the Todd class
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by Jean-Michel Bismut
J. Amer. Math. Soc. 3 (1990), 159-256


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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Bibliographic Information
  • © Copyright 1990 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 3 (1990), 159-256
  • MSC: Primary 58G12; Secondary 32L10, 57R20, 58G05, 58G11
  • DOI:
  • MathSciNet review: 1017783