{
  "abstract": "Let $S$ be a closed translation surface of genus $g\\ge 2$ with $\\mathop{area}(S)= 4πg$. We show that for any $λ\\in (0, 1)$ there exist $\\lfloor λ\\cdot g\\rfloor$ homologically independent simple closed curves of length at most $ C(λ) \\cdot \\log(g)$, where $C(λ)$ is a constant that depends only on $λ$. This result is obtained from a mixed graph construction based on a Voronoi graph of the surface with the cone points as seeds and its dual graph. We also give a complementary result using only the Voronoi graph that produces $2g$ short loops that form a homology basis. This construction, however, depends on the length of a shortest saddle connection of the surface $S$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30561",
  "author_total": 4,
  "authors": [
    {
      "name": "Peter Buser"
    },
    {
      "name": "Achintya Dey"
    },
    {
      "name": "Eran Makover"
    },
    {
      "name": "Bjoern Muetzel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/brhtx7hyp6nb2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30561",
  "fulltext_url": null,
  "id": "brhtx7hyp6nb2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30561",
  "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.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7214650951",
  "pdf_url": "https://arxiv.org/pdf/2609.30561",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/brhtx7hyp6nb2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2609.30561",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30561"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Short homology bases for translation surfaces",
  "title_text": "Short homology bases for translation surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/brhtx7hyp6nb2",
  "venue": "arXiv",
  "versions": []
}