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

22 Apr 2020  ·  Kubota Yosuke, Schick Thomas ·

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. read more

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K-Theory and Homology Geometric Topology Operator Algebras