### 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).

Original language | English (US) |
---|---|

Pages (from-to) | 3671-3699 |

Number of pages | 29 |

Journal | Geometry and Topology |

Volume | 22 |

Issue number | 6 |

DOIs | |

State | Published - Sep 23 2018 |

### All Science Journal Classification (ASJC) codes

- Geometry and Topology

## Fingerprint Dive into the research topics of 'C<sup>*</sup> –algebraic higher signatures and an invariance theorem in codimension two'. Together they form a unique fingerprint.

## Cite this

Higson, N., Schick, T., & Xie, Z. (2018). C

^{*}–algebraic higher signatures and an invariance theorem in codimension two.*Geometry and Topology*,*22*(6), 3671-3699. https://doi.org/10.2140/gt.2018.22.3671