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The local index formula in semifinite von Neumann algebras II: The even case
Authors:Alan L Carey  Adam Rennie
Institution:a Mathematical Sciences Institute, Australian National University, Canberra, ACT 0200, Australia
b Department of Mathematics and Statistics, University of Victoria, Room D227, Clearihue Building, 3800 Finnerty Road (Ring Road), Victoria, BC, Canada V8W 3P4
c School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia
d School of Informatics and Engineering, Flinders University, Bedford Park, SA 5042, Australia
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.
Keywords:primary 19K56  46L80  secondary 58B30  46L87
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