{"paper":{"title":"Volume invariant and maximal representations of discrete subgroups of Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Inkang Kim, Sungwoon Kim","submitted_at":"2012-05-22T01:55:58Z","abstract_excerpt":"Let $\\Gamma$ be a lattice in a connected semisimple Lie group $G$ with trivial center and no compact factors. We introduce a volume invariant for representations of $\\Gamma$ into $G$, which generalizes the volume invariant for representations of uniform lattices introduced by Goldman. Then, we show that the maximality of this volume invariant exactly characterizes discrete, faithful representations of $\\Gamma$ into $G$ except for $\\Gamma\\subset \\mathrm{PSL_2 \\mathbb{C}}$ a nonuniform lattice."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4787","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":""},"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"}