{"paper":{"title":"On the deck groups of iterates of bicritical rational maps","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Kathryn Lindsey, Sarah Koch, Thomas Sharland","submitted_at":"2022-10-06T18:10:01Z","abstract_excerpt":"Given a rational map $f:\\widehat{\\mathbb C}\\to\\widehat{\\mathbb C}$ on the Riemann sphere, we define $\\mathrm{Deck}(f)$ to be the group of M\\\"obius transformations $\\mu$ satisfying $f \\circ \\mu = f$. In this note, we consider the groups $\\mathrm{Deck}(f^k)$, where $f$ is a \\emph{bicritical} rational map (that is, a rational map with exactly two critical points) and $f^k$ denotes the $k$th iterate of $f$. In particular, we give a complete description of which groups (up to isomorphism) arise as the groups $\\mathrm{Deck}(f^k)$ for bicritical rational maps $f$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.03148","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2210.03148/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}