{
  "abstract": "We explicitly determine the complex bordism class of the $n$-th symmetric product of a complex curve of genus $g$. In particular, we provide an explicit formula expressing this class as an integral linear combination of bordism classes of products of complex projective spaces. Similarly, we determine the unoriented bordism class of the $n$-th symmetric product of a non-orientable surface of genus $g$ (i.e., $\\#_{i=1}^{g+1}\\mathbb R P^2$). It turns out that these classes are also expressed as a $\\mathbb Z_2$-linear combination of bordism classes of products of even-dimensional real projective spaces. We also give an affirmative answer to a non-orientable version of the Blagojević--Grujić--Živaljević conjecture stating that the topological type of any symmetric product of a noncompact surface of finite type determines the topological type of the surface itself.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07813",
  "author_total": 2,
  "authors": [
    {
      "name": "Georgy Chernykh"
    },
    {
      "name": "Dmitry Gugnin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5rj55w9cv958m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07813",
  "fulltext_url": null,
  "id": "5rj55w9cv958m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07813",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07813",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5rj55w9cv958m.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07813",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07813"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On bordism classes of symmetric products of surfaces",
  "title_text": "On bordism classes of symmetric products of surfaces",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:48Z",
  "url": "https://research.draconitic.com/paper/5rj55w9cv958m",
  "venue": "arXiv",
  "versions": []
}