Robustness of topological phases on aperiodic lattices
Operator Algebras
2026-03-24 v2 Mathematical Physics
K-Theory and Homology
math.MP
Abstract
We study the robustness of topological phases on aperiodic lattices by constructing *-homomorphisms from the groupoid model to the coarse-geometric model of observable C*-algebras. These *-homomorphisms induce maps in K-theory and Kasparov theory. We show that the strong topological phases in the groupoid model are detected by position spectral triples. We show that topological phases coming from stacking along another Delone set are always weak in the coarse-geometric sense.
Keywords
Cite
@article{arxiv.2504.04817,
title = {Robustness of topological phases on aperiodic lattices},
author = {Yuezhao Li},
journal= {arXiv preprint arXiv:2504.04817},
year = {2026}
}
Comments
Revised version. 34 pages, 2 figures. To appear in Math. Phys. Anal. Geom