{"paper":{"title":"A complex of ribbon quivers and $\\mathcal{M}_{g,m}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.AG","authors_text":"Sergei Merkulov","submitted_at":"2025-03-03T19:53:30Z","abstract_excerpt":"For any integer $d\\in \\mathbb{Z}$ we introduce a complex $\\mathsf{ORGC}_{d}^{(g,m)}$ spanned by genus $g$ ribbon quivers with $m$ marked boundaries and prove that its cohomology computes (up to a degree shift) the compactly supported cohomology of the moduli space $\\mathcal{M}_{g,m}$ of genus $g$ algebraic curves with $m$ marked points.\n  We show that the totality of complexes $$ \\mathsf{orgc}_{d}= \\prod_{g\\geq 1} \\mathsf{ORGC}_{d}^{(g,1)}{\\simeq} \\prod_{g\\geq 1} H_c^{\\bullet-1+2g(d-1)}(\\mathcal{M}_{g,1}) $$ has a natural dg Lie algebra structure which controls the deformation theory of the dg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.02020","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/2503.02020/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"}