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

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 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.

12 pages. v2 final version to appear in G&T. Small corrections and minor changes of presentation

References in corpus (2)

• The topology of positive scalar curvature
• The relative Mishchenko--Fomenko higher index and almost flat bundles II: Almost flat index pairing

Cited by in corpus (4)

• Width, Largeness and Index Theory
• The bulk-dislocation correspondence for weak topological insulators on screw-dislocated lattices
• Codimension 2 transfer of higher index invariants
• Band width and the Rosenberg index