Index theory and topological phases of aperiodic lattices

Bourne, C.; Mesland, B.

doi:10.1007/s00023-019-00764-9

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Index theory and topological phases of aperiodic lattices

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Mesland, B.
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s00023-019-00764-9
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arXiv:1807.03972.pdf
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Citation

Bourne, C., & Mesland, B. (2019). Index theory and topological phases of aperiodic lattices. Annales Henri Poincaré, 20(6), 1969-2038. doi:10.1007/s00023-019-00764-9.

Cite as: https://hdl.handle.net/21.11116/0000-0004-85DE-C

Abstract

We examine the non-commutative index theory associated with the dynamics of a Delone set and the corresponding transversal groupoid. Our main motivation comes from the application to topological phases of aperiodic lattices and materials and applies to invariants from tilings as well. Our discussion concerns semifinite index pairings, factorisation
properties of Kasparov modules and the construction of unbounded Fredholm modules for lattices with finite local complexity.