{
  "abstract": "We prove that the $Q$th symmetric product of an absolute $λ$-Lipschitz retract, equipped with the bottleneck matching metric, is an absolute $(3Q-2)λ$-Lipschitz retract. This answers a question of De Pauw about the target spaces of Almgren's $Q$-valued maps. We also prove that the space of nonempty subsets with at most $n$ points, equipped with the Hausdorff metric, is an absolute $(6n-5)λ$-Lipschitz retract. The main tool is a reconstruction theorem for bounded products of metric stars with finitely many rays, modulo a finite permutation group: these quotients are absolute $3$-Lipschitz retracts, independently of the group and the number of coordinates. A variant of this theorem, in which unordered sets of sign vectors take the place of the group action, handles finite subset spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10976",
  "author_total": 1,
  "authors": [
    {
      "name": "Leonid V. Kovalev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7293ewnf1zg7a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10976",
  "fulltext_url": null,
  "id": "7293ewnf1zg7a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10976",
  "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.MG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7221094943",
  "pdf_url": "https://arxiv.org/pdf/2610.10976",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7293ewnf1zg7a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.10976",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10976"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Symmetric products and finite subset spaces of absolute Lipschitz retracts",
  "title_text": "Symmetric products and finite subset spaces of absolute Lipschitz retracts",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/7293ewnf1zg7a",
  "venue": "arXiv",
  "versions": []
}