Abstract
The goal of the heat kernel method is to express (2.40) as an integral over the fixed point set Mγ in M of the transformation γ. Here Mγ = 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].
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© 2011 Springer Science+Business Media, LLC
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Duistermaat, J.J. (2011). The Heat Kernel Method. In: The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator. Modern Birkhäuser Classics. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-8247-7_7
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DOI: https://doi.org/10.1007/978-0-8176-8247-7_7
Publisher Name: Birkhäuser Boston
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Online ISBN: 978-0-8176-8247-7
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