Kubo Formulas and Bulk-Edge Correspondence for Curved Boundaries
Abstract
Strong topological insulators are classified by integer invariants which admit different real-space expressions. Inspired by recent work studying these invariants for spaces with curved boundaries, we revisit the problem of equivalence of the various expressions, including Fredholm index pairings and Kubo formulas involving half-space projections. Using Roe algebras and a variant of KK-theory suitable for non-separable C*-algebras, we prove a general form of bulk-edge correspondence for the index pairing with a general position-space Dirac operator in the presence of arbitrary boundaries. For spaces coarsely equivalent to ℝd, we show that up to multiplicity, these pairings are equal to those obtained with the standard dual Dirac operator, with the multiplicity explicitly given as the topological degree of the symbol function. In addition, we prove a generalized Kubo formula which computes the general index pairing by a real-space formula.
Related
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BibTeX
@misc{martinian2026kubo,
title = {{Kubo Formulas and Bulk-Edge Correspondence for Curved Boundaries}},
author = {Aren Martinian and Tom Stoiber},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29524},
eprint = {2608.29524},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29524},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Kubo Formulas and Bulk-Edge Correspondence for Curved Boundaries
AU - Aren Martinian
AU - Tom Stoiber
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29524
UR - https://arxiv.org/abs/2608.29524
AB - Strong topological insulators are classified by integer invariants which admit different real-space expressions. Inspired by recent work studying these invariants for spaces with curved boundaries, we revisit the problem of equivalence of the various expressions, including Fredholm index pairings and Kubo formulas involving half-space projections. Using Roe algebras and a variant of KK-theory suitable for non-separable C^*-algebras, we prove a general form of bulk-edge correspondence for the index pairing with a general position-space Dirac operator in the presence of arbitrary boundaries. For spaces coarsely equivalent to ℝ^d, we show that up to multiplicity, these pairings are equal to those obtained with the standard dual Dirac operator, with the multiplicity explicitly given as the topological degree of the symbol function. In addition, we prove a generalized Kubo formula which computes the general index pairing by a real-space formula.
ER -