Volume 22, issue 6 (2018)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 22
Issue 6, 3145–3760
Issue 5, 2511–3144
Issue 4, 1893–2510
Issue 3, 1267–1891
Issue 2, 645–1266
Issue 1, 1–644

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
$C^*$–algebraic higher signatures and an invariance theorem in codimension two

Nigel Higson, Thomas Schick and Zhizhang Xie

Geometry & Topology 22 (2018) 3671–3699
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).

Keywords
$K$–theory, $C^*$–algebraic signature, partitioned manifold theorem, eventual homotopy equivalence
Mathematical Subject Classification 2010
Primary: 19K56, 57R19
References
Publication
Received: 12 October 2017
Accepted: 2 April 2018
Published: 23 September 2018
Proposed: Benson Farb
Seconded: Tobias H Colding, Martin Bridson
Authors
Nigel Higson
Department of Mathematics
Pennsylvania State University
University Park, PA
United States
Thomas Schick
Mathematisches Institut
Georg-August-Universität Göttingen
Göttingen
Germany
Zhizhang Xie
Department of Mathematics
Texas A&M University
College Station, TX
United States