arXiv subjects

Yuezhao Li

Publications and source records attributed to Yuezhao Li.

3 recordsLinked to original sources

arXiv2026

Consistent symmetry breaking and topological phases

Operators invariant under a symmetry group are also invariant under any finite-index subgroup. The equivariant indices of such operators must be consistent under symmetry breaking. We use this principle to establish a canonical weak/strong dichotomy for equivariant indices, building on an idea originating in the theory of topological insulators in solid-state physics. We also study the relationship to coarse-geometric, or macroscopic, indices.

math-ph↗

arXiv2025

The odd spectral localiser via asymptotic morphisms and quasi-projections

We describe the index pairing between an odd K-theory class and an odd unbounded Kasparov module by a pair of quasi-projections, supported on a submodule obtained from a finite spectral truncation. We achieve this by pairing the K-theory class with an asymptotic morphism determined by the unbounded Kasparov module. We interpret the spectral localiser of Loring and Schulz-Baldes as an instance of such an index pairing.

math.KT↗

arXiv2025

Robustness of topological phases on aperiodic lattices

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.

math.OA↗