{"paper":{"title":"Twisted Conjugacy in Big Mapping Class Groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Sushil Bhunia, Swathi Krishna","submitted_at":"2021-12-13T12:48:42Z","abstract_excerpt":"Let $G$ be a group and $\\varphi$ be an automorphism of $G$. Two elements $x, y$ of $G$ are said to be $\\varphi$-twisted conjugate if $y=gx\\varphi(g)^{-1}$ for some $g\\in G$. A group $G$ has the $R_{\\infty}$-property if the number of $\\varphi$-twisted conjugacy classes is infinite for every automorphism $\\varphi$ of $G$. In this paper we prove that the big mapping class group $MCG(S)$ possesses the $R_{\\infty}$-property under some suitable conditions on the infinite-type surface $S$. As an application we also prove that the big mapping class group possesses the $R_\\infty$-property if and only i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.06612","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/2112.06612/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"}