{"paper":{"title":"Contractible flow of stability conditions via global dimension function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Yu Qiu","submitted_at":"2020-08-01T15:26:49Z","abstract_excerpt":"We introduce an analytic method that uses the global dimension function $\\operatorname{gldim}$ to produce contractible flows on the space $\\operatorname{Stab}\\mathcal{D}$ of stability conditions on a triangulated category $\\mathcal{D}$. In the case when $\\mathcal{D}=\\mathcal{D}(\\mathbf{S}^\\lambda)$ is the topological Fukaya category of a graded surface $\\mathbf{S}^\\lambda$, we show that $\\operatorname{gldim}^{-1}(0,y)$ contracts to $\\operatorname{gldim}^{-1}(0,x)$ for any $1\\le x\\le y$, provided $(x,y)$ does not contain `critical' values $\\{1+w_\\partial/m_\\partial \\mid w_\\partial\\ge0, \\partial"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.00282","kind":"arxiv","version":5},"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/2008.00282/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"}