{
  "abstract": "We introduce a metric geometry on the space of positive, linearly growing quasimorphisms on a mixing subshift of finite type. Two such quasimorphisms are identified when their homogenizations agree up to multiplicative scaling. The resulting moduli space carries a natural symmetrised Thurston-type metric, defined from the extremal ratios of their periodic orbit lengths. We prove that this is a genuine metric and determine several global features of the resulting space: it is unbounded, separable, incomplete, and has geodesics that are canonically generated by thermodynamic pressure functions. We then describe the endpoints of these geodesics and develop a boundary theory for our moduli space. We apply this theory to metric structures on right-angled Artin and Coxeter groups. In particular we construct isometric embeddings of geometric moduli spaces into our quasimorphism moduli spaces. As a consequence, Manhattan curves for metrics on these groups are $C^1$, with equality cases characterised by rough similarity of the underlying metrics. This provides insights into Manhattan curves in settings where neither classical thermodynamic formalism for Hölder potentials nor Patterson-Sullivan theory apply. The same construction recovers the corresponding results for hyperbolic groups and places these examples within a common dynamical-geometric framework.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26778",
  "author_total": 4,
  "authors": [
    {
      "name": "Stephen Cantrell"
    },
    {
      "name": "Pablo Carrasco"
    },
    {
      "name": "Emilio Corso"
    },
    {
      "name": "Federico Rodriguez Hertz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a2bscnafd3f16.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26778",
  "fulltext_url": null,
  "id": "a2bscnafd3f16",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26778",
  "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.DS"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
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  "openalex": "W7223005853",
  "pdf_url": "https://arxiv.org/pdf/2610.26778",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a2bscnafd3f16.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:31:00Z",
      "native_id": "2610.26778",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26778"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The moduli space of quasimorphisms on subshifts and its pressure geometry",
  "title_text": "The moduli space of quasimorphisms on subshifts and its pressure geometry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:47Z",
  "url": "https://research.draconitic.com/paper/a2bscnafd3f16",
  "venue": "arXiv",
  "versions": []
}