{"paper":{"title":"Higgs bundles over cell complexes and representations of finitely generated groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Chikako Mese, George Daskalopoulos, Graeme Wilkin","submitted_at":"2016-05-16T01:05:13Z","abstract_excerpt":"The purpose of this paper is to extend the Donaldson-Corlette theorem to the case of vector bundles over cell complexes. We define the notion of a vector bundle and a Higgs bundle over a complex, and describe the associated Betti, de Rham and Higgs moduli spaces. The main theorem is that the $SL(r, \\mathbb{C})$ character variety of a finitely presented group $\\Gamma$ is homeomorphic to the moduli space of rank $r$ Higgs bundles over an admissible complex $X$ with $\\pi_1(X) = \\Gamma$. A key role is played by the theory of harmonic maps defined on singular domains."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04625","kind":"arxiv","version":1},"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"}