{"paper":{"title":"The bounded Borel class and complex representations of 3-manifold groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Alessandra Iozzi, Marc Burger, Michelle Bucher","submitted_at":"2014-12-10T19:50:46Z","abstract_excerpt":"If $\\Gamma<\\mathrm{PSL}(2,\\mathbb{C})$ is a lattice, we define an invariant of a representation $\\Gamma\\rightarrow \\mathrm{PSL}(n,\\mathbb{C})$ using the Borel class $\\beta(n)\\in \\mathrm{H}^3_\\mathrm{c}(\\mathrm{PSL}(n,\\mathbb{C}),\\mathbb{R})$. We show that the invariant is bounded and its maximal value is attained by conjugation of the composition of the lattice embedding with the irreducible complex representation $\\mathrm{PSL}(2,\\mathbb{C})\\rightarrow \\mathrm{PSL}(n,\\mathbb{C})$.\n  Major ingredients of independent interest are the extension to degenerate configuration of flags of a Goncharov "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3428","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"}