K-homology, assembly and rigidity theorems for relative eta invariants

Nigel Higson, John Roe

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

We connect the assembly map in C*-algebra K-theory to rigidity properties for relative eta invariants that have been investigated by Mathai, Keswani, Weinberger and others. We give a new and conceptual proof of Keswani's theorem that whenever the C*-algebra assembly map is an iso- morphism, the relative eta invariants associated to the signature operator are homotopy invariants, whereas the relative eta invariants associated to the Dirac operator on a manifold with positive scalar curvature vanish.

Original languageEnglish (US)
Pages (from-to)555-601
Number of pages47
JournalPure and Applied Mathematics Quarterly
Volume6
Issue number2
DOIs
StatePublished - Apr 2010

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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