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The local index formula in semifinite Von Neumann algebras I: Spectral flow |
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| Authors: | Alan L Carey Adam Rennie |
| Institution: | a Mathematical Sciences Institute, Australian National University, Canberra, ACT. 0200, Australia b Department of Mathematics and Statistics, University of Victoria, Victoria, B.C., Canada V8W 3P4 c School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW, 2308 Australia d School of Informatics and Engineering, Flinders University, Bedford Park S.A., 5042 Australia |
| Abstract: | We generalise the local index formula of Connes and Moscovici to the case of spectral triples for a *-subalgebra A of a general semifinite von Neumann algebra. In this setting it gives a formula for spectral flow along a path joining an unbounded self-adjoint Breuer-Fredholm operator, affiliated to the von Neumann algebra, to a unitarily equivalent operator. Our proof is novel even in the setting of the original theorem and relies on the introduction of a function valued cocycle which is ‘almost’ a (b,B)-cocycle in the cyclic cohomology of A. |
| Keywords: | primary: 19K56 46L80 secondary: 58B30 46L87 |
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