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

Authors

Alan L. Carey, Australian National University
John Phillips, University of Victoria
Adam C. Rennie, University of NewcastleFollow
F A. Sukochev, Flinders University

RIS ID

77527

Publication Details

Carey, A. L., Rennie, A. C., Phillips, J. & Sukochev, F. A. (2006). The local index formula in semifinite von Neumann algebras II: the even case. Advances in Mathematics, 202 (2), 517-554.

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.