74 citations · 652 across the 48 of their papers we have counts for
5 papers · 1 filter
Non-Commutative Vector Bundles for Non-Unital Algebras
Adam Rennie, Aidan Sims
We revisit the characterisation of modules over non-unital -algebras analogous to modules of sections of vector bundles. A fullness condition on the associated multiplier modu…
Chern numbers, localisation and the bulk-edge correspondence for continuous models of topological phases
Chris Bourne, Adam Rennie
In order to study continuous models of disordered topological phases, we construct an unbounded Kasparov module and a semifinite spectral triple for the crossed product of a separa…
Boundaries, spectral triples and K-homology
Iain Forsyth, Magnus Goffeng, Bram Mesland +1
This paper extends the notion of a spectral triple to a relative spectral triple, an unbounded analogue of a relative Fredholm module for an ideal . Examples incl…
The Cuntz-Pimsner extension and mapping cone exact sequences
Francesca Arici, Adam Rennie
For Cuntz-Pimsner algebras of bi-Hilbertian bimodules of finite Jones-Watatani index satisfying some side conditions, we give an explicit isomorphism between the -theory exact s…
The -theoretic bulk-edge correspondence for topological insulators
Chris Bourne, Johannes Kellendonk, Adam Rennie
We study the application of Kasparov theory to topological insulator systems and the bulk-edge correspondence. We consider observable algebras as modelled by crossed products, wher…