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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].

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)
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