Flat vector bundles, direct images and higher real analytic torsion

Bismut, Jean-Michel; Lott, John

doi:10.1090/S0894-0347-1995-1303026-5

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

DOI: https://doi.org/10.1090/S0894-0347-1995-1303026-5

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Abstract:

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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