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2018 $C^*$–algebraic higher signatures and an invariance theorem in codimension two
Nigel Higson, Thomas Schick, Zhizhang Xie
Geom. Topol. 22(6): 3671-3699 (2018). DOI: 10.2140/gt.2018.22.3671

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).

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Nigel Higson. Thomas Schick. Zhizhang Xie. "$C^*$–algebraic higher signatures and an invariance theorem in codimension two." Geom. Topol. 22 (6) 3671 - 3699, 2018. https://doi.org/10.2140/gt.2018.22.3671

Information

Received: 12 October 2017; Accepted: 2 April 2018; Published: 2018
First available in Project Euclid: 29 September 2018

zbMATH: 06945134
MathSciNet: MR3858772
Digital Object Identifier: 10.2140/gt.2018.22.3671

Subjects:
Primary: 19K56, 57R19

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.22 • No. 6 • 2018
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