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Spectral flow and Dixmier traces. (English) Zbl 1015.19003
The authors show how the Dixmier trace can be calculated in terms of the asymptotics of the zeta function and of the heat operator in a general semi-finite von Neumann algebra. As applications, they deduce a formula for the Chern character of an odd \({\mathcal L}^{(1,\infty)}\)-summable Breuer-Fredholm module in terms of a Hochschild 1-cycle and explain how to derive a Wodzicki residue for pseudo-differential operators along the orbits of an ergodic \({\mathbb R}^n\)-action on a compact space.

MSC:
19K56 Index theory
46L80 \(K\)-theory and operator algebras (including cyclic theory)
46L87 Noncommutative differential geometry
58B34 Noncommutative geometry (à la Connes)
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