On the Strong Novikov Conjecture of Locally Compact Groups for Low Degree Cohomology Classes
On the Strong Novikov Conjecture of Locally Compact Groups for Low Degree Cohomology Classes
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DOI：
10.14989/doctor.k20046
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发表时间：
2016-04
期刊：
影响因子：
--
通讯作者：
Yoshiyasu Fukumoto
中科院分区：
文献类型：
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作者：
Yoshiyasu Fukumoto
本文的主要结果是索引映射的图像不消失，从适当的$G$-紧致$G$-流形$X$的$G$-等变$K$-同调到群$G$的$C^{*}$-代数的$K$-理论。假设$K$-同调类与低维上同调类的克罗内克配对非零，我们证明该类在索引图下的图像非零。既不需要局部紧群 $G$ 的离散性，也不需要 $G$ 对 $X$ 的作用的自由性。 B. Hanke 和 T. Schick 早些时候考虑过离散群体自由行动的情况。
The main result of this paper is non-vanishing of the image of the index map from the $G$-equivariant $K$-homology of a proper $G$-compact $G$-manifold $X$ to the $K$-theory of the $C^{*}$-algebra of the group $G$. Under the assumption that the Kronecker pairing of a $K$-homology class with a low-dimensional cohomology class is non-zero, we prove that the image of this class under the index map is non-zero. Neither discreteness of the locally compact group $G$ nor freeness of the action of $G$ on $X$ are required. The case of free actions of discrete groups was considered earlier by B. Hanke and T. Schick.