{
  "abstract": "We present an $\\infty$-categorical refinement of classical $KK$-theory and $E$-theory for graded, $G$-equivariant for a locally compact second countable group $G$, Real $C^*$-algebras. As a consequence, we obtain a couple of fiber sequences connecting the different $K$-theory spectra, and explicitly analyse the induced endomorphisms on $K_0$-groups. We also answer precisely some folklore questions in the area. Among other things, we show that graded $KK$- and $E$-categories are not a Dwyer-Kan localization of graded $C^*$-algebras.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17060",
  "author_total": 1,
  "authors": [
    {
      "name": "Anupam Datta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3fphhewbz4z7a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17060",
  "fulltext_url": null,
  "id": "3fphhewbz4z7a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17060",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AT"
    ],
    [
      "arxiv",
      "math.KT"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7221772916",
  "pdf_url": "https://arxiv.org/pdf/2610.17060",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3fphhewbz4z7a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17060",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17060"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.KT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A higher categorical approach to graded bivariant $K$-theories for Real $C^*$-algebras",
  "title_text": "A higher categorical approach to graded bivariant K-theories for Real C^*-algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/3fphhewbz4z7a",
  "venue": "arXiv",
  "versions": []
}