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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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Flat vector bundles, direct images and higher real analytic torsion
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by Jean-Michel Bismut and John Lott
J. Amer. Math. Soc. 8 (1995), 291-363


We prove a Riemann-Roch-Grothendieck-type theorem concerning the direct image of a flat vector bundle under a submersion of smooth manifolds. We refine this theorem to the level of differential forms. We construct associated secondary invariants, the analytic torsion forms, which coincide in degree 0 with the Ray-Singer real analytic torsion. Résumé. On démontre un analogue du théorème de Riemann-Roch-Grothendieck pour l’image directe d’un fibré plat par une submersion. On raffine ce théorème au niveau des formes différentielles. On construit des invariants secondaires, les formes de torsion analytique, qui coïncident, en degré 0, avec la torsion de Ray-Singer.
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Bibliographic Information
  • © Copyright 1995 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 8 (1995), 291-363
  • MSC: Primary 58G26; Secondary 58G11
  • DOI:
  • MathSciNet review: 1303026