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arXiv 1710.020902017-10-05math.KTmath.ATmath.GT

C*-Algebraic Higher Signatures and an Invariance Theorem in Codimension Two

Nigel Higson, Thomas Schick, Zhizhang Xie

备注：: 30 pages
发表信息：: Geom. Topol. 22 (2018) 3671-3699
DOI：: 10.2140/gt.2018.22.3671

英文摘要：

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 of 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).

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