54 citations · 124 across the 11 of their papers we have counts for
5 papers · 1 filter
A noncommutative Atiyah-Patodi-Singer index theorem in KK-theory
A. L. Carey, J. Phillips, A. Rennie
We investigate an extension of ideas of Atiyah-Patodi-Singer (APS) to a noncommutative geometry setting framed in terms of Kasparov modules. We use a mapping cone construction to r…
Semifinite spectral triples associated with graph C*-algebras
Alan Carey, John Phillips, Adam Rennie
We review the recent construction of semifinite spectral triples for graph C^*-algebras. These examples have inspired many other developments and we review some of these such as th…
Orbifolds are not commutative geometries
Adam Rennie, Joseph C. Varilly
In this note we show that the crucial orientation condition for commutative geometries fails for the natural spectral triple of an orbifold M/G.
Noncommutative manifolds from graph and -graph -algebras
David Pask, Adam Rennie, Aidan Sims
In previous papers, we constructed smooth (1,\infty)-summable semfinite spectral triples for graph algebras with a faithful trace, and (k,\infty)-summable semifinite spectral tripl…
KK-theory and Spectral Flow in von Neumann Algebras
Jens Kaad, Ryszard Nest, Adam Rennie
We present a definition of spectral flow relative to any norm closed ideal J in any von Neumann algebra N. Given a path D(t) of selfadjoint operators in N which are invertible in N…