{
  "abstract": "Parlier proved that there exists a constant $U>0$ such that for any hyperbolic surface $S$ of genus $g$ with systole $\\ell$ the following holds: \\[ Kiss(S)\\leq U \\frac {e^\\ell}\\ell g \\] where $Kiss(S)$ is the maximum number of homotopically distinct systoles in $S$ (Kissing number). We show that there exists a constant $V>0$ and a sequence $S_n$ of hyperbolic homogeneous surfaces of genus $g_n\\to \\infty$ with a bounded systole such that \\[ Kiss(S_n)\\geq Vg_n \\] for all $n\\geq 1$. This shows that Parlier's theorem is sharp for a fixed systole length. Our proof uses Bruhat--Tits buildings of type $\\tilde A_2$ and Hamiltonian surfaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24222",
  "author_total": 2,
  "authors": [
    {
      "name": "S. Barré"
    },
    {
      "name": "M. Pichot"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0s827axtmzhr7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24222",
  "fulltext_url": null,
  "id": "0s827axtmzhr7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24222",
  "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.GR"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7223030295",
  "pdf_url": "https://arxiv.org/pdf/2610.24222",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0s827axtmzhr7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24222",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24222"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On the kissing number of hyperbolic surfaces with a small systole",
  "title_text": "On the kissing number of hyperbolic surfaces with a small systole",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/0s827axtmzhr7",
  "venue": "arXiv",
  "versions": []
}