{"paper":{"title":"A question of Norton-Sullivan in the analytic case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hui Yang, Jian Wang","submitted_at":"2018-09-19T16:22:56Z","abstract_excerpt":"In 1996, A. Norton and D. Sullivan asked the following question: If $f:\\mathbb{T}^2\\rightarrow\\mathbb{T}^2$ is a diffeomorphism, $h:\\mathbb{T}^2\\rightarrow\\mathbb{T}^2$ is a continuous map homotopic to the identity, and $h f=T_{\\rho} h$ where $\\rho\\in\\mathbb{R}^2$ is a totally irrational vector and $T_{\\rho}:\\mathbb{T}^2\\rightarrow\\mathbb{T}^2,\\, z\\mapsto z+\\rho$ is a translation, are there natural geometric conditions (e.g. smoothness) on $f$ that force $h$ to be a homeomorphism? In [ J. Wang and Z. Zhang, GAFA 2018 ], the first author and Z. Zhang gave a negative answer to the above question"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07284","kind":"arxiv","version":1},"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"}