{"paper":{"title":"Conjugacy classes in M\\\"obius groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Krishnendu Gongopadhyay","submitted_at":"2009-10-10T14:24:06Z","abstract_excerpt":"Let $\\H^{n+1}$ denote the $n + 1$-dimensional (real) hyperbolic space. Let $\\s^{n}$ denote the conformal boundary of the hyperbolic space. The group of conformal diffeomorphisms of $\\s^n$ is denoted by $M (n)$. Let $M_o (n)$ be its identity component which consists of all orientation-preserving elements in $M (n)$. The conjugacy classification of isometries in $M_o (n)$ depends on the conjugacy of $T$ and $T^{-1}$ in $M_o (n)$. For an element $T$ in $M (n)$, $T$ and $T^{-1}$ are conjugate in $M (n)$, but they may not be conjugate in $M_o (n)$. In the literature, $T$ is called real if $T$ is co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1909","kind":"arxiv","version":4},"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"}