{
  "abstract": "We consider a wide class of $2D$ tight - binding models of solid state physics. These models are, in the most general case, non - homogeneous. The topological invariant ${\\cal N}_3$ responsible for the quantization of the Hall conductivity, for the specific case of the integer quantum Hall effect in $2D$, is expressed through the Wigner transformation of the two-point electron Matsubara Green function. We express this invariant as a pairing of the element of the $K^{-1}$ group (generated by the Green function) with the specific element of the cyclic cohomology group $HC^3$. According to a set of local index theorems the values of ${\\cal N}_3$ can be shown to be integer for a limited class of tight - binding models. We concentrate on systems with a spectral gap, with the chemical potential inside the gap and an invertible Dirac operator $\\hat Q$ throughout the Matsubara-frequency domain. The mobility-gap case is not considered here and will be addressed in forthcoming publications.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.08868",
  "author_total": 5,
  "authors": [
    {
      "name": "G. Kovyrshin"
    },
    {
      "name": "A. Mekrami"
    },
    {
      "name": "J. Miller"
    },
    {
      "name": "M. A. Zubkov"
    },
    {
      "name": "A. Zuevsky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d3wfmsssetcw8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.08868",
  "fulltext_url": null,
  "id": "d3wfmsssetcw8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.08868",
  "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.MP"
    ],
    [
      "openalex",
      "3107|Topological Materials and Phenomena"
    ]
  ],
  "openalex": "W7164019552",
  "pdf_url": "https://arxiv.org/pdf/2606.08868",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d3wfmsssetcw8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:53Z",
      "native_id": "2606.08868",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.08868"
    }
  ],
  "subjects": [
    {
      "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"
    }
  ],
  "title": "Topological invariant responsible for the integer QHE and non-commutative geometry",
  "title_text": "Topological invariant responsible for the integer QHE and non-commutative geometry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/d3wfmsssetcw8",
  "venue": "arXiv",
  "versions": []
}