## The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac OperatorReprinted as it originally appeared in the 1990s, this work is as an affordable text that will be of interest to a range of researchers in geometric analysis and mathematical physics. The book covers a variety of concepts fundamental to the study and applications of the spin-c Dirac operator, making use of the heat kernels theory of Berline, Getzlet, and Vergne. True to the precision and clarity for which J.J. Duistermaat was so well known, the exposition is elegant and concise. |

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### Contents

Chapter 2 The DolbeaultDirac Operator | 7 |

Chapter 3 Clifford Modules | 18 |

Chapter 4 The Spin Group and the Spinc Group | 35 |

Chapter 5 The Spinc Dirac Operator | 41 |

Chapter 6 Its Square | 52 |

Chapter 7 The Heat Kernel Method | 69 |

Chapter 8 The Heat Kernel Expansion | 77 |

Chapter 9 The Heat Kernel on a Principal Bundle | 98 |

Chapter 11 The HirzebruchRiemannRoch Integrand | 130 |

Chapter 12 The Local Lefschetz Fixed Point Formula | 147 |

Chapter 13 Characteristic Classes | 157 |

Chapter 14 The Orbifold Version | 171 |

Chapter 15 Application to Symplectic Geometry | 187 |

Equivariant Forms | 220 |

Bibliography | 237 |

245 | |

### Other editions - View all

The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator J.J. Duistermaat No preview available - 2011 |

The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator Johannes Jisse Duistermaat No preview available - 1996 |

### Common terms and phrases

action of G asymptotic expansion automorphism Chern Clifford algebra coadjoint coefficients commutes compact complex analytic complex linear complex structure connected component connection form covariant differentiation defined denotes diagonal differential forms eigenvalues element equal equation equivariantly factor fiber finite Fixed Point Formula fixed point set G-action G-invariant geodesic Hamiltonian heat kernel Heat Kernel Lefschetz Hermitian structure homomorphism horizontal implies infinitesimal action inner product integral kernel invariant isomorphism J.J. Duistermaat Kähler manifold Kernel Lefschetz Fixed Laplace operator Lefschetz Fixed Point Lemma Levi-Civita connection Lie algebra Lie group linear mapping Modern Birkhäuser Classics momentum mapping neighborhood notation orbifold orbifold chart orbit orthogonal orthonormal basis orthonormal frame polynomial principal symbol proof reduced phase space respect Riemannian structure sections smooth manifold SOFM Spin spin-c Dirac operator Spin(V Springer Science+Business Media subspace supertrace tangent space Theorem tracec two-form unique unitary frame vector field whor zero