"In the early 1980's topologists and geometers for the first time came across unfamiliar words like C*-algebras and von Neumann algebras through the discovery of new knot invariants (by V.F.R. Jones) or through a remarkable result on the relationship between characteristic class…
Through classification of compact abelian group actions on semifinite injective factors, Jones and Takesaki introduced a notion of an action of a measured groupoid on a von Neumann algebra, which was proven to be an important tool for such an analysis. In this paper, elaborating…
The object of this paper is to define a natural analytic index function on an arbitrary von Neumann algebra relative to an arbitrary ideal. This index map enables us to develop a complete Fredholm and semi-Fredholm theory in this setting which is parallel to classical Fredholm a…
