{"paper":{"title":"Geometry and quasisymmetric parametrization of Semmes spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.MG","authors_text":"Jang-Mei Wu, Pekka Pankka","submitted_at":"2011-11-09T13:09:46Z","abstract_excerpt":"We consider decomposition spaces $\\R^3/G$ that are manifold factors and admit defining sequences consisting of cubes-with-handles. Metrics on $\\R^3/G$ constructed via modular embeddings into Euclidean spaces promote the controlled topology to a controlled geometry. The quasisymmetric parametrizability of the metric space $\\R^3/G\\times \\R^m$ imposes quantitative topological constraints, in terms of the circulation and growth, to the defining sequences for $\\R^3/G$. We give a necessary condition and a sufficient condition for the existence of parametrization. The necessary condition answers a qu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2197","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}