{
  "abstract": "We study the topological band theory of quantum Hall systems in which the adiabatic flux parameters of an external gauge potential form a high-dimensional manifold. This situation arises both for strongly correlated matter on spatial Riemann surfaces of genus $g > 1$, as well as in the formal study of matter on compact oriented manifolds of dimension $4\\ell+2 = 2p$ coupled to $p$-form gauge potentials. In these cases, the underlying topological invariants defined over the parameter space are significantly richer than the low-dimensional (i.e., two-dimensional) case and involve both the curvature (i.e., first Chern class) as well as higher order curvature invariants. These higher curvature invariants correspond to topologically protected contributions to Kubo-like formulae, constructed from correlation functions of the physical current operators. We illustrate these general considerations with an explicit example from hyperbolic band theory based on the genus-two Bolza Riemann surface, a case which has recently been simulated on a synthetic-dimension platform.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35977",
  "author_total": 4,
  "authors": [
    {
      "name": "Vivek Chakrabhavi"
    },
    {
      "name": "Walt Chavarria"
    },
    {
      "name": "Jonathan J. Heckman"
    },
    {
      "name": "Steven Rayan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/26s28fe7cypjw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35977",
  "fulltext_url": null,
  "id": "26s28fe7cypjw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35977",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mes-hall"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Topological Materials and Phenomena"
    ]
  ],
  "openalex": "W7214891696",
  "pdf_url": "https://arxiv.org/pdf/2609.35977",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/26s28fe7cypjw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.35977",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35977"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mes-hall",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Topological Band Theory for High-Dimensional Parameter Spaces",
  "title_text": "Topological Band Theory for High-Dimensional Parameter Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/26s28fe7cypjw",
  "venue": "arXiv",
  "versions": []
}