The Heat Kernel Method
J. J. Duistermaat · Birkhäuser Boston eBooks · 1996
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 = E ⊗ L , 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]. 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.