Enlargeability and index theory: infinite covers

Abstract

Abstract. In [5] we showed non-vanishing of the universal index elements in the K-theory of the maximal C∗-algebras of the fun-damental groups of enlargeable spin manifolds. The underlying notion of enlargeability was the one from [3], involving contracting maps defined on finite covers of the given manifolds. In the paper at hand, we weaken this assumption to the one in [4] where infinite covers are allowed. The new idea is the construction of a geomet-rically 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. 1. Overview of results This paper is a sequel to [5]. We quickly review the relevant math-ematics and the motivation for our research. Since the work of Lich-nerowicz it has been known that index theory can be used to construct computable obstructions to the existence of positive scalar curvature