74 citations · 322 across the 15 of their papers we have counts for
15 papers
Analytic index theory and spectral flow in real Hilbert -modules
Chris Bourne, Alan L. Carey, Koen van den Dungen +1
We consider the analytic index and spectral flow of Fredholm operators on Hilbert -modules. Our spaces and algebras are equipped with a real structure, so the analytic index a…
Index Theory of Chiral Unitaries and Split-Step Quantum Walks
Chris Bourne
Building from work by Cedzich et al. and Suzuki et al., we consider topological and index-theoretic properties of chiral unitaries, which are an abstraction of the time evolution o…
Locally equivalent quasifree states and index theory
Chris Bourne
We consider quasifree ground states of Araki's self-dual CAR algebra from the viewpoint of index theory and symmetry protected topological (SPT) phases. We first review how Cliffor…
Localised module frames and Wannier bases from groupoid Morita equivalences
Chris Bourne, Bram Mesland
Following the operator algebraic approach to Gabor analysis, we construct frames of translates for the Hilbert space localisation of the Morita equivalence bimodule arising from a…
The classification of symmetry protected topological phases of one-dimensional fermion systems
Chris Bourne, Yoshiko Ogata
We introduce an index for symmetry protected topological (SPT) phases of infinite fermionic chains with an on-site symmetry given by a finite group . This index takes values in…
The Cayley transform in complex, real and graded -theory
Chris Bourne, Johannes Kellendonk, Adam Rennie
We use the Cayley transform to provide an explicit isomorphism at the level of cycles from van Daele -theory to -theory for graded -algebras with a real structure. Isom…