可扩展性和指数理论：无限覆盖
Enlargeability and index theory: Infinite covers
摘要：
在前一篇文章中，我们证明了可扩张自旋流形的基本群的极大C*-代数的K-理论中的泛指标元的非零性。可扩性的基本概念来自Gromov和Lawson的第一篇相关论文，涉及定义在给定流形的有限覆盖上的收缩映射。在本文中，我们将这个假设减弱为Gromov和Lawson的第二篇论文中的假设，其中允许无限覆盖。新的想法是构造一个几何给定的C*-代数与跟踪编码的信息，这些无限覆盖;一路上，我们得到了一个简单的证明，在这种情况下相关的相对指标定理。
英文摘要：
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.
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