{
  "abstract": "A flag complex $L$ determines a locally CAT(0) cube complex $P_L$ with the links of all vertices isomorphic to $L$. The fundamental group of $P_L$ is the commutator subgroup of the right-angled Coxeter group $W_L$. We observe that an edge contraction $L \\rightarrow L/e$ determines a $2$-fold branched cover $P_L \\rightarrow P_{L/e}$ (up to a homotopy equivalence). We use this branched cover to give an inequality between the $\\mathbb{F}_2$-$L^2$-Betti numbers of $W_L$ and $W_{L/e}$. This reduces an $\\mathbb{F}_2$-version of the Singer Conjecture for right-angled Coxeter groups to minimal flag triangulations of even dimensional spheres. We also use this inequality to compute the $L^2$-Betti numbers of $W_L$ when $L$ is a flag triangulation of the projective plane or the torus.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02723",
  "author_total": 3,
  "authors": [
    {
      "name": "Grigori Avramidi"
    },
    {
      "name": "Boris Okun"
    },
    {
      "name": "Kevin Schreve"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5htqa9xeem8hc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02723",
  "fulltext_url": null,
  "id": "5htqa9xeem8hc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02723",
  "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"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7220382169",
  "pdf_url": "https://arxiv.org/pdf/2610.02723",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5htqa9xeem8hc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02723",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02723"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Reflections on branched covers",
  "title_text": "Reflections on branched covers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/5htqa9xeem8hc",
  "venue": "arXiv",
  "versions": []
}