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2021 The Gromov–Lawson codimension $2$ obstruction to positive scalar curvature and the $C^*$–index
Yosuke Kubota, Thomas Schick
Geom. Topol. 25(2): 949-960 (2021). DOI: 10.2140/gt.2021.25.949

Abstract

Gromov and Lawson developed a codimension 2 index obstruction to positive scalar curvature for a closed spin manifold M, later refined by Hanke, Pape and Schick. Kubota has shown that this obstruction also can be obtained from the Rosenberg index of the ambient manifold M, which takes values in the K–theory of the maximal C–algebra of the fundamental group of M, using relative index constructions.

In this note, we give a slightly simplified account of Kubota’s work and remark that it also applies to the signature operator, thus recovering the homotopy invariance of higher signatures of codimension 2 submanifolds of Higson, Schick and Xie.

Citation

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Yosuke Kubota. Thomas Schick. "The Gromov–Lawson codimension $2$ obstruction to positive scalar curvature and the $C^*$–index." Geom. Topol. 25 (2) 949 - 960, 2021. https://doi.org/10.2140/gt.2021.25.949

Information

Received: 3 October 2019; Revised: 19 March 2020; Accepted: 19 April 2020; Published: 2021
First available in Project Euclid: 28 May 2021

Digital Object Identifier: 10.2140/gt.2021.25.949

Subjects:
Primary: 19K56 , 46L80 , 58J22

Keywords: $C^*$–index theory , higher index theory , higher signature , positive scalar curvature

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.25 • No. 2 • 2021
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