Enlargeability and index theory: Infinite covers
Enlargeability and index theory: Infinite covers
复制标题
可扩展性和索引理论：无限覆盖
DOI：
10.1007/s10977-007-9004-3
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
T. Schick
中科院分区：
文献类型：
--
作者：
B. Hanke;T. Schick
在上一篇文章中，我们证明了可放大自旋流形基本群的极大C*-代数的k理论中普遍指标元素的不消性。放大性的基本概念来自Gromov和Lawson的第一篇相关论文，涉及在给定流形的有限覆盖上定义的收缩映射。在这篇论文中，我们将这一假设弱化为Gromov和Lawson第二篇论文中的假设，其中允许无限覆盖。新的思想是构造一个几何给定的C*-代数，它带有迹来编码这些无限覆盖所给出的信息；在此过程中，我们得到了一个与此相关的相对指标定理的简单证明。
In a previous paper, we showed nonvaninishing of the universal index elements in the K-theory of the maximal C*-algebras of the fundamental groups of enlargeable spin manifolds. The underlying notion of enlargeability was the one from the first relevant paper of Gromov and Lawson, involving contracting maps defined on finite covers of the given manifolds. In the paper at hand, we weaken this assumption to the one in the second paper of Gromov and Lawson, where infinite covers are allowed. The new idea is the construction of a geometrically given C*-algebra with trace which encodes the information given by these infinite covers; along the way we obtain an easy proof of a relative index theorem relevant in this context.