{
  "annotation_id": "13b3efe9-3079-4a82-80a3-36ba29ff043c",
  "date_created": "2026-02-17T05:53:12.491000Z",
  "date_modified": "2026-02-17T05:53:12.491000Z",
  "file_hash": "de517192079a6935a15e4b6344e157e5c4a89efc4739ae282c94e94cbdee4af7",
  "private": false,
  "record": {
    "abstract": "We introduce asymptotic-M\\\"obius (AM) maps, a large-scale analogue of quasi-M\\\"obius maps tailored to geometric group theory. AM-maps capture coarse cross-ratio behavior for configurations of points that lie far apart, providing a notion of \"conformality at infinity\" that is stable under quasi-isometries, compatible with scaling limits, and rigid enough to yield structural consequences absent from Pansu\u0027s notion of large-scale conformality. We establish basic properties of AM-maps, give several sources of examples, including quasi-isometries, sublinear bi-Lipschitz equivalences, snowflaking, and Assouad embeddings, and apply the theory to large-scale dimension and metric cotype. As applications we obtain dimension-monotonicity results for nilpotent groups and CAT(0) spaces, and new obstructions to the existence of AM-maps arising from metric cotype.",
    "arxiv_id": "2601.07702",
    "authors": [
      "Georg Gr\u00fctzner"
    ],
    "categories": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Asymptotic-M\\\"obius maps",
    "url": "https://arxiv.org/abs/2601.07702",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5ba3cd1b-d9e3-4aa2-bf4f-6af8cb2f218f",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}