5 papers
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…
The KO-valued spectral flow for skew-adjoint Fredholm operators
Chris Bourne, Alan L. Carey, Matthias Lesch +1
In this article we give a comprehensive treatment of a `Clifford module flow' along paths in the skew-adjoint Fredholm operators on a real Hilbert space that takes values in KO${}_…
On -indices for ground states of fermionic chains
Chris Bourne, Hermann Schulz-Baldes
For parity-conserving fermionic chains, we review how to associate -indices to ground states in finite systems with quadratic and higher-order interactions as well as…
Index theory and topological phases of aperiodic lattices
Chris Bourne, Bram Mesland
We examine the noncommutative index theory associated to the dynamics of a Delone set and the corresponding transversal groupoid. Our main motivation comes from the application to…