{"paper":{"title":"Tagged mapping class groups: Auslander-Reiten translation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.RT","authors_text":"Thomas Br\\\"ustle, Yu Qiu","submitted_at":"2012-11-30T21:00:04Z","abstract_excerpt":"We give a geometric realization, the tagged rotation, of the AR-translation on the generalized cluster category associated to a surface $\\mathbf{S}$ with marked points and non-empty boundary, which generalizes Br\\\"{u}stle-Zhang's result for the puncture free case.\n  As an application, we show that the intersection of the shifts in the 3-Calabi-Yau derived category $\\mathcal{D}(\\Gamma_{\\mathbf{S}})$ associated to the surface and the corresponding Seidel-Thomas braid group of $\\mathcal{D}(\\Gamma_{\\mathbf{S}})$ is empty, unless $\\mathbf{S}$ is a polygon with at most one puncture (i.e. of type A o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0007","kind":"arxiv","version":3},"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"}