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The Local Index Formula In Noncommutative Geometry Revisited, Alan Carey, John Phillips, Adam Rennie, Fyodor Sukochev

Associate Professor Adam Rennie

In this review we discuss the local index formula in noncommutative geomety from the viewpoint of two new proofs are partly inspired by the approach of Higson especially that in but they differ in several fundamental aspedcts, in particular they apply to semifinite spectral triples for a *s-subalgebra A of a general semifinite von Neumann algebra. Our proofs are novel even in the setting of the original theorem and reduce the hypotheses of the theorem to those necessary for its statement. These proofs rely on the introduction of a function valued cocycle which is 'almost' a (b, B)-cocycle in the …