{
  "abstract": "Let G be a linear group with Kazhdan property (T) generated by d elements. We show that there are generating sets of size d+2 with arbitrarily small Kazhdan constants. We also prove the same conclusion for every finitely generated group admitting a non-elementary convergence action on a compact metrizable space. This includes non-elementary word-hyperbolic and relatively hyperbolic groups, as well as finitely generated non-elementary subgroups of word-hyperbolic groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36098",
  "author_total": 3,
  "authors": [
    {
      "name": "Tsachik Gelander"
    },
    {
      "name": "Alex Lubotzky"
    },
    {
      "name": "Jvbin Yao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6s7wak9g5bh1p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36098",
  "fulltext_url": null,
  "id": "6s7wak9g5bh1p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36098",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7214975649",
  "pdf_url": "https://arxiv.org/pdf/2609.36098",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6s7wak9g5bh1p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.36098",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36098"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Small Kazhdan constants for small generating sets of linear groups",
  "title_text": "Small Kazhdan constants for small generating sets of linear groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/6s7wak9g5bh1p",
  "venue": "arXiv",
  "versions": []
}