{"paper":{"title":"Flat connections and resonance varieties: from rank one to higher ranks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.GR"],"primary_cat":"math.AT","authors_text":"Alexander I. Suciu, Clement Radu Popescu, Daniela Anca Macinic, Stefan Papadima","submitted_at":"2013-12-05T05:39:26Z","abstract_excerpt":"Given a finitely-generated group $\\pi$ and a linear algebraic group $G$, the representation variety Hom$(\\pi,G)$ has a natural filtration by the characteristic varieties associated to a rational representation of $G$. Its algebraic counterpart, the space of $\\mathfrak{g}$-valued flat connections on a commutative, differential graded algebra $(A,d)$ admits a filtration by the resonance varieties associated to a representation of $\\mathfrak{g}$. We establish here a number of results concerning the structure and qualitative properties of these embedded resonance varieties, with particular attenti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1439","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"}