2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73062We 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.53 pages, to appear in Advances in MathematicsOperator AlgebrasK-Theory and Homologytext