927 citations
- Australian Mathematical Sciences InstituteAU17 papers
- Centre for Ultrahigh Bandwidth Devices for Optical SystemsAU16 papers
- Mount Stromlo ObservatoryAU10 papers
- The University of AdelaideAU9 papers
- Institute for Physics of MicrostructuresRU8 papers
- California Institute of TechnologyUS7 papers
- Centre National de la Recherche ScientifiqueFR6 papers
- European Southern ObservatoryCL6 papers
- Joint Institute for Nuclear AstrophysicsUS6 papers
- Massachusetts Institute of TechnologyUS6 papers
- Michigan State UniversityUS6 papers
- National Astronomical Observatory of JapanJP6 papers
9 papers · 1 filter
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.
Operator integrals, spectral shift and spectral flow
N. A. Azamov, A. L. Carey, P. G. Dodds +1
We present a new and simple approach to the theory of multiple operator integrals that applies to unbounded operators affiliated with general von Neumann algebras. For semifinite v…
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…
The Local Index Formula in Semifinite von Neumann Algebras II: The Even Case
Alan L. Carey, John Phillips, Adam Rennie +1
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…