TY - JOUR

T1 - C* –algebraic higher signatures and an invariance theorem in codimension two

AU - Higson, Nigel

AU - Schick, Thomas

AU - Xie, Zhizhang

N1 - Funding Information:
Acknowledgements The authors would like to thank the Centre International de Rencontres Mathématiques, and the organizers of the 2015 CIRM Conference on Noncommutative Geometry, where their work together began. Xie is partially supported by NSF 1500823, NSF 1800737, and NSFC 11420101001.
Publisher Copyright:
© 2018, Mathematical Sciences Publishers. All rights reserved.

PY - 2018/9/23

Y1 - 2018/9/23

N2 - 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).

AB - 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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U2 - 10.2140/gt.2018.22.3671

DO - 10.2140/gt.2018.22.3671

M3 - Article

AN - SCOPUS:85054548472

SN - 1465-3060

VL - 22

SP - 3671

EP - 3699

JO - Geometry and Topology

JF - Geometry and Topology

IS - 6

ER -