Communications in Mathematical Physics

, Volume 115, Issue 1, pp 79–126 | Cite as

Analytic torsion and holomorphic determinant bundles

II. Direct images and Bott-Chern forms
  • Jean-Michel Bismut
  • Henri Gillet
  • Christophe Soulé


In this paper, we derive the main properties of Kähler fibrations. We introduce the associated Levi-Civita superconnection to construct analytic torsion forms for holomorphic direct images. These forms generalize in any degree the analytic torsion of Ray and Singer. In the case of acyclic complexes of holomorphic Hermitian vector bundles, such forms are calculated by means of Bott-Chern classes.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Vector Bundle 
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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Jean-Michel Bismut
    • 1
  • Henri Gillet
    • 2
  • Christophe Soulé
    • 3
  1. 1.Département de MathématiqueUniversité Paris-SudOrsay CedexFrance
  2. 2.Department of MathematicsUniversity of Illinois at ChicagoChicagoUSA
  3. 3.C.N.R.S., L.A. 212 and IHESBures/YvetteFrance

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