## Bott and Duistermaat-Herckman Formulas

In Chapter One we have defined characteristic classes and numbers. A natural question is hoe to compute these characteristic numbers. Let $\omega$ be a characteristic form on an even dimensional smooth closed oriented manifold $M$. If
$\omega=\omega_{[1]}+\omega_{[2]}+\cdots+\omega_{[\dim M]},\quad \omega_{[i]}\in\Omega^{i}(M), i=1,\cdots,\dim M,$ then the characteristic number associated $\omega$ is defined by $\int_{M}\omega=\int_M\omega_{[\dim M]}$. The Bott’s result shows that
$\int_M\omega_{[\dim M]}=\sum_{p\in A}\mu(P),$

## 如何在LaTeX中制作动画

1. 制作frame, 也就是帧, 我们知道动画都是连续播放静态图片而运动起来的. Continue Reading

## 2009中科大数学分析

1. 判断
1. $\sum_{n=0}^{+\infty}\frac{(1+2i)^n}{3^n-2^n}$的收敛性.
2. $f$ 一致收敛的充要条件是 $f$ 把 Cauchy 列映成 Cauchy 列.