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The
Gromov–Lawson codimension $2$ obstruction to positive scalar
curvature and the $C^*$–index
Yosuke Kubota and Thomas Schick |
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Geometry & Topology 25 (2021) 949–960
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Abstract |
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Gromov and Lawson developed a codimension index obstruction to positive scalar curvature for a closed spin manifold , 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 , which takes values in the K–theory of the maximal –algebra of the fundamental group of , 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 submanifolds of Higson, Schick and Xie. |
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Keywords
higher index theory, positive scalar curvature, higher
signature, $C^*$–index theory
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Mathematical Subject Classification 2010
Primary: 19K56, 46L80, 58J22
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References |
Publication
Received: 3 October 2019
Revised: 19 March 2020
Accepted: 19 April 2020
Published: 27 April 2021
Proposed: John Lott
Seconded: David M Fisher, Bruce Kleiner
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Authors |
| Yosuke Kubota | |
| Department of Mathematical
Sciences Shinshu University Matsumoto Japan |
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| Thomas Schick | |
| Mathematisches Institut Universität Göttingen Göttingen Germany |
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| http://www.uni-math.gwdg.de/schick | |
