{"paper":{"title":"Reducing conjugacy in the full diffeomorphism group of R to conjugacy in the subgroup of orientation-preserving maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DS","authors_text":"Anthony G. O'Farrell, Maria Roginskaya","submitted_at":"2008-11-20T16:29:21Z","abstract_excerpt":"Let $\\Diffeo=\\Diffeo(\\R)$ denote the group of infinitely-differentiable diffeomorphisms of the real line $\\R$, under the operation of composition, and let $\\Diffeo^+$ be the subgroup of diffeomorphisms of degree +1, i.e. orientation-preserving diffeomorphisms. We show how to reduce the problem of determining whether or not two given elements $f,g\\in \\Diffeo$ are conjugate in $\\Diffeo$ to associated conjugacy problems in the subgroup $\\Diffeo^+$. The main result concerns the case when $f$ and $g$ have degree -1, and specifies (in an explicit and verifiable way) precisely what must be added to t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.3370","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"}