Translator Disclaimer
2016 The surgery exact sequence, K-theory and the signature operator
Paolo Piazza, Thomas Schick
Ann. K-Theory 1(2): 109-154 (2016). DOI: 10.2140/akt.2016.1.109

Abstract

The main result of this paper is a new and direct proof of the natural transformation from the surgery exact sequence in topology to the analytic K-theory sequence of Higson and Roe.

Our approach makes crucial use of analytic properties and new index theorems for the signature operator on Galois coverings with boundary. These are of independent interest and form the second main theme of the paper. The main technical novelty is the use of large-scale index theory for Dirac-type operators that are perturbed by lower-order operators.

Citation

Download Citation

Paolo Piazza. Thomas Schick. "The surgery exact sequence, K-theory and the signature operator." Ann. K-Theory 1 (2) 109 - 154, 2016. https://doi.org/10.2140/akt.2016.1.109

Information

Received: 9 January 2015; Accepted: 7 April 2015; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1335.46063
MathSciNet: MR3514938
Digital Object Identifier: 10.2140/akt.2016.1.109

Subjects:
Primary: 46L80, 46L87, 58J22

Rights: Copyright © 2016 Mathematical Sciences Publishers

JOURNAL ARTICLE
46 PAGES


SHARE
Vol.1 • No. 2 • 2016
MSP
Back to Top