{
  "abstract": "Let $G$ be a finite group. In this article, we develop some results of equivariant persistent homotopy theory for persistent $G$-spaces. We introduce the notions of $G$-stable and $G$-homotopy invariant distances and define the $G$-homotopy interleaving distance, an equivariant analogue $d^G_{HI}$ of the homotopy interleaving distance of Blumberg and Lesnick. We prove that this distance $d^G_{HI}$ is $G$-stable and $G$-homotopy invariant and establish its universality by showing that it dominates any such distance. We further prove a version of equivariant persistent Whitehead theorem relating interleavings of equivariant persistent homotopy groups to $G$-homotopy interleavings of persistent $G$-spaces. We also prove an equivariant persistent nerve lemma for equivariant good covers of persistent $G$-spaces. As a consequence, we obtain an equivariant weak law of large numbers for filtrations, providing a homotopy-theoretic consistency result for random filtrations equipped with finite group of symmetries.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23440",
  "author_total": 3,
  "authors": [
    {
      "name": "Kushal Halder"
    },
    {
      "name": "Subhankar Sau"
    },
    {
      "name": "Debasis Sen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4g2ewabbf4csv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23440",
  "fulltext_url": null,
  "id": "4g2ewabbf4csv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23440",
  "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",
      "math.AT"
    ],
    [
      "openalex",
      "1703|Topological and Geometric Data Analysis"
    ]
  ],
  "openalex": "W7214050431",
  "pdf_url": "https://arxiv.org/pdf/2609.23440",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4g2ewabbf4csv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2609.23440",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23440"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Equivariant Homotopy Interleaving and Persistent Whitehead Theorem",
  "title_text": "Equivariant Homotopy Interleaving and Persistent Whitehead Theorem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/4g2ewabbf4csv",
  "venue": "arXiv",
  "versions": []
}