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Abstract

The goal of the heat kernel method is to express (2.40) as an integral over the fixed point set M γ in M of the transformation γ. Here M γ = M if γ is the identity. The method is based on the following observations about arbitrary elliptic differential operators D, acting on sections of a smooth vector bundle F over a compact manifold M, which admits a a direct sum decomposition F = F + F . In our case, F = EL, with the splitting F ± = E ± L, and D is the spin-c Dirac operator. For the required facts about trace class operators, see for instance Hörmander [42, Sec. 19.1], or Duistermaat [19].

Keywords

Vector Bundle Integral Operator Heat Kernel Integral Kernel Trace Class Operator 
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 Science+Business Media, LLC 2011

Authors and Affiliations

  • J. J. Duistermaat
    • 1
  1. 1.Mathematisch InstituutUniversiteit UtrechtUtrechtThe Netherlands

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