Note on the book Geometry and Analysis on Manifolds

Covering:
   1. Chern-Weil theory in the language of super bundle; localization formulas(Duistermaat-Heckman, Berline-Vergne, etc.); Bott vanishing theorem(adiabatic connection)
  2. Construction of Thom and Euler class(Berezin integral or Clifford action); Gauss-Bonnet-Chern formula through transgression
  3. Analytic proof of Poincare-Hopf formula and Morse inequality(Witten deformation, index of elliptic operator); Kervaire semi-characteristic
  4. Heat kernel and asymptotic expansion; heat equation proof of Gauss-Bonnet-Chern theorem and Hirzebruch theorem(local index formula of operators).