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The Local Index Formula In Noncommutative Geometry Revisited, Alan Carey, John Phillips, Adam Rennie, Fyodor Sukochev
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 …
Semi-Finite Noncommutative Geometry And Some Applications, Alan L. Carey, Adam C. Rennie, John Phillips
Semi-Finite Noncommutative Geometry And Some Applications, Alan L. Carey, Adam C. Rennie, John Phillips
Associate Professor Adam Rennie
These notes are a summary of talks given in Shonan, Japan in February 2008 with modifications from a later series of talks at the Hausdorff Institute for Mathematics in Bonn in July 2008 and at the Erwin Schr¨odinger Institute in October 2008. The intention is to give a short discussion of recent results in noncommutative geometry (NCG) where one extends the usual point of view of [22] by replacing the bounded operators B(H) on a Hilbert space H by certain sub-algebras; namely semi-finite von Neumann algebras. These are weakly closed subalgebras of the bounded operators on a Hilbert space that …