C* –algebraic higher signatures and an invariance theorem in codimension two

Nigel Higson, Thomas Schick, Zhizhang Xie

Research output: Contribution to journalArticle

Abstract

We revisit the construction of signature classes in C*–algebra K–theory, and develop a variation that allows us to prove equality of signature classes in some situations involving homotopy equivalences of noncompact manifolds that are only defined outside a compact set. As an application, we prove a counterpart for signature classes of a codimension-two vanishing theorem for the index of the Dirac operator on spin manifolds (the latter is due to Hanke, Pape and Schick, and is a development of well-known work of Gromov and Lawson).

Original languageEnglish (US)
Pages (from-to)3671-3699
Number of pages29
JournalGeometry and Topology
Volume22
Issue number6
DOIs
StatePublished - Sep 23 2018

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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