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Gromov and Lawson developed a codimension 2 index obstruction to positivescalar curvature for a closed spin manifold M, later refined by Hanke, Pape andSchick. Kubota has shown that also this obstruction can be obtained from theRosenberg index of the ambient manifold M which takes values in the K-theory ofthe maximal C*-algebra of the fundamental group of M, using relative indexconstructions.  In this note, we give a slightly simplified account of Kubota's work andremark that it also applies to the signature operator, thus recovering thehomotopy invariance of higher signatures of codimension 2 submanifolds ofHigson, Schick, Xie.

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