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Communications in Mathematical Physics

, Volume 115, Issue 1, pp 49–78 | Cite as

Analytic torsion and holomorphic determinant bundles I. Bott-Chern forms and analytic torsion

  • J. -M. Bismut
  • H. Gillet
  • C. Soulé
Article

Abstract

We attach secondary invariants to any acyclic complex of holomorphic Hermitian vector bundles on a complex manifold. These were first introduced by Bott and Chern [Bot C]. Our new definition uses Quillen's superconnections. We also give an axiomatic characterization of these classes. These results will be used in [BGS2] and [BGS3] to study the determinant of the cohomology of a holomorphic vector bundle.

Keywords

Neural Network Manifold Statistical Physic Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • J. -M. Bismut
    • 1
  • H. Gillet
    • 2
  • C. Soulé
    • 3
  1. 1.Département de MathématiqueUniversité Paris-SudOrsay CedexFrance
  2. 2.Department of MathematicsUniversity of Illinois at ChicagoChicagoUSA
  3. 3.CNRS LA212 and I.H.E.S.Bures-Sur-YvetteFrance

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