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arXiv · 1710.02090

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

Nigel Higson·Thomas Schick·Zhizhang Xie
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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 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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Nigel Higson, Thomas Schick, Zhizhang Xie. 2017-10-05. C*-Algebraic Higher Signatures and an Invariance Theorem in Codimension Two. https://doi.org/10.2140/gt.2018.22.3671

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