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 $\omega$ is a non-singular 2-form. i.e. If for any $Y\in …
Bott Residue Formula
作者: qinchao
日期: 05/07/2012
没有评论 | 12+
We make the same assumptions as in previous section. Let $i_1,\cdots,i_k$ be $k$ positive even integers. For any $p\in\mathrm{zero}(K)$ and $1\leq j \leq k$, set \[ \lambda^{i_j}(p)=\lambda_1^{i_j}+\cdots+\lambda_l^{i_j}. \]By following theorem, we reduce the computation of characteristic numbers of $TM$ to …
Bott and Duistermaat-Herckman Formulas
作者: qinchao
日期: 04/22/2012
没有评论 | 23+
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), …
2009中科大数学分析
作者: van abel
日期: 04/16/2012
没有评论 | 28+
判断\[\sum_{n=0}^{+\infty}\frac{(1+2i)^n}{3^n-2^n}\]的收敛性.$f$ 一致收敛的充要条件是 $f$ 把 Cauchy 列映成 Cauchy 列.填空$f(x)=1-x$ 在 $x=-1$ 处展开后级数的收敛点集是________;$\sin(x^2)=x$ 有________个根;求 \[ \sum_{k=1}^{+\infty}\left(\frac{1}{2k-1}-\frac{1}{4k-2}-\frac{1}{4k}\right) \] 的和________.$f:[0,1]\to\R$ 单调递增且 $f([0,1])$ 是闭集, 证明 $f$ 在 $[0,1]$ 上连续.$f$ 在 $[0,1]$ 上连续, 且 \[ \int_0^1 f(x)x^n\rd x=0,\quad n=0,1,2,\ldots, \] 证明 $f\equiv0$.是否存在原函数 $F$, 使得 $\rd F$ …
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