Operations in equivariant ℤ/p-cohomology
Operations in equivariant ℤ/p-cohomology
复制标题
等变 ℤ/p-上同调运算
DOI：
--
复制
发表时间：
1999
影响因子：
0.8
通讯作者：
J. Caruso
中科院分区：
文献类型：
--
作者：
J. Caruso
如果G是紧李群，M是Mackey函子，则刘易斯，May和麦克卢尔[4]在G-空间上定义了一个普通的上同调理论H*G（-; M），用表示分次。在本文中，我们计算了整数次稳定运算代数[Ascr ]M的/p-秩，其中G= /p且M在/p处为常数。我们还研究了[Ascr ]M与普通mod-p Steenrod代数[Ascr ] p之间的关系。主要结果意味着，虽然[Ascr ]M相当大，但它在[Ascr ]p中的像仅由单位元和Bockstein组成。这与M常数在m/p的情况形成鲜明对比，其中q = p;有[Ascr ]M <$[Ascr ]q。
If G is a compact Lie group and M a Mackey functor, then Lewis, May and McClure [4] define an ordinary cohomology theory H*G(−; M) on G-spaces, graded by representations. In this article, we compute the ℤ/p-rank of the algebra of integer-degree stable operations [Ascr ]M, in the case where G=ℤ/p and M is constant at ℤ/p. We also examine the relationship between [Ascr ]M and the ordinary mod-p Steenrod algebra [Ascr ]p. The main result implies that while [Ascr ]M is quite large, its image in [Ascr ]p consists of only the identity and the Bockstein. This is in sharp contrast to the case with M constant at ℤ/p for q≠p; there [Ascr ]M≅[Ascr ]q.