The Gromov-Lawson codimension 2 obstruction to positive scalar curvature and the C*-index

Autor:	Kubota, Yosuke, Schick, Thomas
Rok vydání:	2019
Předmět:	Mathematics - K-Theory and Homology Mathematics - Geometric Topology Mathematics - Operator Algebras
Zdroj:	Geom. Topol. 25 (2021) 949-960
Druh dokumentu:	Working Paper
DOI:	10.2140/gt.2021.25.949
Popis:	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 also this obstruction 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, Xie. Comment: 12 pages. v2 final version to appear in G&T. Small corrections and minor changes of presentation
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1909.09584 Zobrazit plný text záznamu View this record from Arxiv