{"paper":{"title":"Reversible biholomorphic germs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Anthony G. O'Farrell, Patrick Ahern","submitted_at":"2008-12-08T21:32:32Z","abstract_excerpt":"Let $G$ be a group. We say that an element $f\\in G$ is {\\em reversible in} $G$ if it is conjugate to its inverse, i.e. there exists $g\\in G$ such that $g^{-1}fg=f^{-1}$. We denote the set of reversible elements by $R(G)$. For $f\\in G$, we denote by $R_f(G)$ the set (possibly empty) of {\\em reversers} of $f$, i.e. the set of $g\\in G$ such that $g^{-1}fg=f^{-1}$. We characterise the elements of $R(G)$ and describe each $R_f(G)$, where $G$ is the the group of biholomorphic germs in one complex variable. That is, we determine all solutions to the equation $ f\\circ g\\circ f = g$, in which $f$ and $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.1575","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"}