Spectral flow and winding number in von Neumann algebras
نویسنده
چکیده
We define a new topology, weaker than the gap topology, on the space of selfadjoint operators affiliated to a semifinite von Neumann algebra and define the real-valued spectral flow for a continuous path of selfadjoint Breuer-Fredholm operators in terms of a generalization of the winding number. We compare our definition with Phillips’ analytical definition. Furthermore we prove the homotopy invariance of the real-valued index. We also prove that the real-valued spectral flow of a path of invariant symmetric elliptic differential operators on a Galois covering with coefficients depending continuously on the parameter is well-defined.
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