{
  "abstract": "This paper studies Veech groups of dilation surfaces whose fundamental group is not finitely generated. We prove that if $ S$ is a surface with self-similar end space and every end is accumulated by genus, then every countable subgroup of $SL(2,\\mathbb{R}) $ can be realized as the Veech group of a dilation surface homeomorphic to $ S$. Additionally, we can construct this dilation surface such that it realizes horizon saddle connections in a prescribed set of directions. This contrasts with the case of closed dilation surfaces, where horizon saddle connections impose restrictions on the algebraic structure of the Veech group.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31447",
  "author_total": 1,
  "authors": [
    {
      "name": "Oscar Rutilio Molina Medrano"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3qzfxjtqk439h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31447",
  "fulltext_url": null,
  "id": "3qzfxjtqk439h",
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  "landing_url": "https://arxiv.org/abs/2609.31447",
  "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.GR"
    ],
    [
      "arxiv",
      "math.GT"
    ],
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      "openalex",
      "2610|Mathematical Dynamics and Fractals"
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  "openalex": "W7214617347",
  "pdf_url": "https://arxiv.org/pdf/2609.31447",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3qzfxjtqk439h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.31447",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31447"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Horizon saddle connections and Veech groups of infinite-type dilation surfaces",
  "title_text": "Horizon saddle connections and Veech groups of infinite-type dilation surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/3qzfxjtqk439h",
  "venue": "arXiv",
  "versions": []
}