Duistermaat-Heckman Formula and Bott’s Original Idea

1. Duistermaat-Heckman Formula In this section, we consider the case of that $\left(M^{2l},\omega\right)$ is a symplectic manifold. Let $(M,\omega)$ be a symplectic manifold with $\omega$ is a symplectic structure. It means

  1. $\omega$ is a non-singular 2-form. i.e. If for any $Y\in \Gamma(TM)$ there always have $\omega(X,Y)=0$, then $X=0$.
  2. $\rd \omega=0$.
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