{
  "abstract": "We determine the $RO(C_2)$-graded $k\\mathbb R$-Hurewicz image, where $k \\mathbb R$ denotes the connective Atiyah's Real $K$-theory spectrum. As a consequence, we obtain four infinite families in the $RO(C_2)$-graded equivariant stable stems that are $C_2$-equivariant refinements of the classical $μ$-families. Using a $C_2$-equivariant $v_{1,0}$-self map, we explicitly construct an equivariant Adams periodicity operator $P_{C_2}$ that captures these $v_1$-periodicity phenomena in the $C_2$-stable stems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19606",
  "author_total": 5,
  "authors": [
    {
      "name": "Sihao Ma"
    },
    {
      "name": "Xiaolin Danny Shi"
    },
    {
      "name": "Zhouli Xu"
    },
    {
      "name": "Albert Jinghui Yang"
    },
    {
      "name": "Shangjie Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a91ag6vnt16wy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19606",
  "fulltext_url": null,
  "id": "a91ag6vnt16wy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19606",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7222308866",
  "pdf_url": "https://arxiv.org/pdf/2610.19606",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a91ag6vnt16wy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19606",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19606"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The $RO(C_2)$-graded Hurewicz image of Atiyah's Real K-theory",
  "title_text": "The RO(C_2)-graded Hurewicz image of Atiyah's Real K-theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/a91ag6vnt16wy",
  "venue": "arXiv",
  "versions": []
}