The local index formula in semifinite von Neumann algebras II: the even case

Abstract

We generalise the even local index formula of Connes and Moscovici to the case of spectral triples for a*-subalgebra A of a general semifinite von Neumann algebra. The proof is a variant of that for the odd case which appears in Part I. To allow for algebras with a non-trivial centre we have to establish a theory of unbounded Fredholm operators in a general semifinite von Neumann algebra and in particular prove a generalised McKean-Singer formula.