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$C^*$–algebraic higher
signatures and an invariance theorem in codimension two
Nigel Higson, Thomas Schick and Zhizhang Xie |
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Geometry & Topology 22 (2018) 3671–3699
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Abstract |
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We revisit the construction of signature classes in –algebra –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). |
Keywords
$K$–theory, $C^*$–algebraic signature, partitioned manifold
theorem, eventual homotopy equivalence
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Mathematical Subject Classification 2010
Primary: 19K56, 57R19
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References |
Publication
Received: 12 October 2017
Accepted: 2 April 2018
Published: 23 September 2018
Proposed: Benson Farb
Seconded: Tobias H Colding, Martin Bridson
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Authors |
| Nigel Higson | |
| Department of Mathematics Pennsylvania State University University Park, PA United States |
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| Thomas Schick | |
| Mathematisches Institut Georg-August-Universität Göttingen Göttingen Germany |
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| Zhizhang Xie | |
| Department of Mathematics Texas A&M University College Station, TX United States |
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