{
  "abstract": "Let $\\mathbb{Z}[1/n] := \\{a/n^r: a \\in \\mathbb{Z},r \\in \\mathbb{Z} \\geq 0\\}$ be the euclidean domain obtained from the ring of integers $\\mathbb{Z}$ by localizing at $n$. Moreover, let $\\text{SL}_2(\\mathbb{Z}[1/n])$ be the group of all invertible 2-by-2 matrices of determinant one with entries in $\\mathbb{Z}[1/n]$. The homology groups $H_k(\\text{SL}_2(\\mathbb{Z}[1/n]),\\mathbb{Z})$ are of interest in Geometric Group Theory, Algebraic Number Theory and Algebraic K-theory. In this dissertation, we study these groups via a spectral sequence derived by the action of $\\text{SL}_2(\\mathbb{Z}[1/n])$ on the product of the trees $B_p$ associated with the $p$-adic valuation on $\\mathbb{Q}$ where $p$ is a prime factor of $n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.25633",
  "author_total": 1,
  "authors": [
    {
      "name": "Isadora Vanzella Picinini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7wm344gkmkzby.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.25633",
  "fulltext_url": null,
  "id": "7wm344gkmkzby",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.25633",
  "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.AT"
    ],
    [
      "arxiv",
      "math.KT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7204452630",
  "pdf_url": "https://arxiv.org/pdf/2608.25633",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7wm344gkmkzby.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2608.25633",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.25633"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.KT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The integral homology of $\\text{SL}_2(\\mathbb{Z}[1/n])$",
  "title_text": "The integral homology of SL_2(ℤ[1/n])",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/7wm344gkmkzby",
  "venue": "arXiv",
  "versions": []
}