Enlargeability and index theory: Infinite covers

Abstract

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.

14 pages, comma in author field added, to appear in K-theory

References in corpus (3)

• A counterexample to the (unstable) Gromov-Lawson-Rosenberg conjecture
• Enlargeability and index theory
• Remarks on a conjecture of Gromov and Lawson

Cited by in corpus (12)

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• Codimension two index obstructions to positive scalar curvature
• Band width estimates via the Dirac operator
• Coarse topology, enlargeability, and essentialness
• Large scale index of multi-partitioned manifolds
• Enlargeable metrics on nonspin manifolds
• Twisted K-theory and obstructions against positive scalar curvature metrics
• Scalar curvature and vector bundles
• Spectral flow of Callias operators, odd K-cowaist, and positive scalar curvature
• An appendix to a paper by B. Hanke and T. Schick
• Scalar curvature rigidity and the higher mapping degree
• Thomsen's D-theory and the K-theoretic Kronecker pairing