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Chris Bourne
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The K-Theoretic Bulk–Edge Correspondence for Topological Insulators
C Bourne, J Kellendonk, A Rennie
Annales Henri Poincaré 18 (5), 1833-1866, 2017
742017
Non-commutative Chern numbers for generic aperiodic discrete systems
C Bourne, E Prodan
Journal of Physics A: Mathematical and Theoretical 51 (23), 235202, 2018
652018
A non-commutative framework for topological insulators
C Bourne, AL Carey, A Rennie
Reviews in Mathematical Physics 28 (02), 1650004, 2016
602016
Chern numbers, localisation and the bulk-edge correspondence for continuous models of topological phases
C Bourne, A Rennie
Mathematical Physics, Analysis and Geometry 21 (3), 16, 2018
402018
The bulk-edge correspondence for the quantum Hall effect in Kasparov theory
C Bourne, AL Carey, A Rennie
Letters in Mathematical Physics 105 (9), 1253-1273, 2015
352015
The classification of symmetry protected topological phases of one-dimensional fermion systems
C Bourne, Y Ogata
Forum of Mathematics, Sigma 9, 2021
272021
Index theory and topological phases of aperiodic lattices
C Bourne, B Mesland
Annales Henri Poincaré 20 (6), 1969-2038, 2019
182019
On ℤ 2-indices for ground states of fermionic chains
C Bourne, H Schulz-Baldes
Reviews in Mathematical Physics 32 (9), 2050028, 2020
122020
Topological states of matter and noncommutative geometry
C Bourne
The Australian National University, 2015
102015
The KO-valued spectral flow for skew-adjoint Fredholm operators
C Bourne, AL Carey, M Lesch, A Rennie
Journal of Topology and Analysis 14 (2), 505-556, 2020
92020
Application of semifinite index theory to weak topological phases, in 2016 MATRIX Annals, MATRIX Book Ser., Vol. 1
C Bourne, H Schulz-Baldes
arXiv preprint arXiv:1612.01613, 203-227, 2018
8*2018
Localised module frames and Wannier bases from groupoid Morita equivalences
C Bourne, B Mesland
Journal of Fourier Analysis and Applications 27 (69), 2021
7*2021
The Cayley transform in complex, real and graded -theory
C Bourne, J Kellendonk, A Rennie
International Journal of Mathematics 31 (9), 2050074, 2020
72020
Locally equivalent quasifree states and index theory
C Bourne
Journal of Physics A: Mathematical and Theoretical 55 (10), 104004, 2022
52022
Index theory of chiral unitaries and split-step quantum walks
C Bourne
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 19, 053, 2023
32023
The K-theoretic classification of topological insulators and superconductors
C Bourne
2023
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