The Pontrjagin class of an orbit space
The Pontrjagin class of an orbit space
复制标题
轨道空间的庞特雅金级
DOI：
10.1016/0040-9383(72)90012-2
复制
发表时间：
1972
期刊：
影响因子：
--
通讯作者：
D. Zagier
中科院分区：
文献类型：
--
作者：
D. Zagier
其中Sign （g， X）是在[i1]中定义的（对于偶维X，对于奇维X为零）等变签名。左边是L （X/G）的顶维分量，所以我们期望整个类L (X/G)（通过投影提升到X）将由G中某个等变L类L (G， X) EH*（X； C）的平均值给出(2)这实际上是定理的形式。第1节将给出该定理的公式，第2节将给出其证明，第3节将包含Bott研究的同调流形的应用，第4节将讨论对称积。
where Sign (g, X) is the equivariant signature defined (for X of even dimension; for X odddimensional it is zero) and studied in [I 1. The left-hand side of this is the top-dimensional component of L (X/G), so we expect that the whole class L (X/G)(lifted up to X by the projection) will be given by the average over g in G of some equivariant L-class L (g, X) EH*(X; C).(2)This is in fact the form that the theorem will take. The formulation of the theorem will be given in Section 1 and its proof in Section 2, while Section 3 contains the application to the homology manifold studied by Bott and Section 4 the discussion of symmetric products.