Bojarski, Bogdan; Weber, Andrzej Correspondences and index. (English) Zbl 1123.58013 Bojarski, Bogdan (ed.) et al., \(C^*\)-algebras and elliptic theory. Basically formed by contributions from the international conference, Bȩdlewo, Poland, February 2004. In cooperation with Dan Burghelea, Richard Melrose and Victor Nistor. Basel: Birkhäuser (ISBN 3-7643-7686-4/hbk). Trends in Mathematics, 1-21 (2006). The authors define a suitable class of correspondences of polarized representations of \(C^\ast\)-algebras, which are modeled on the spaces of boundary values of elliptic operators on bordisms joining two manifolds. In that setup, the index is defined and its additivity is studied.For the entire collection see [Zbl 1097.58001]. Reviewer: Dian K. Palagachev (Bari) MSC: 58J32 Boundary value problems on manifolds 47A53 (Semi-) Fredholm operators; index theories 35J55 Systems of elliptic equations, boundary value problems (MSC2000) 35Q15 Riemann-Hilbert problems in context of PDEs 55N15 Topological \(K\)-theory 58J20 Index theory and related fixed-point theorems on manifolds 46L05 General theory of \(C^*\)-algebras 46L80 \(K\)-theory and operator algebras (including cyclic theory) Keywords:index of an elliptic operator; Riemann-Hilbert problem; bordism; \(K\)-theory PDFBibTeX XMLCite \textit{B. Bojarski} and \textit{A. Weber}, in: \(C^*\)-algebras and elliptic theory. Basically formed by contributions from the international conference, Bȩdlewo, Poland, February 2004. In cooperation with Dan Burghelea, Richard Melrose and Victor Nistor. Basel: Birkhäuser. 1--21 (2006; Zbl 1123.58013) Full Text: arXiv