{"paper":{"title":"Higgs bundles and higher Teichm\\\"uller spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Oscar Garc\\'ia-Prada","submitted_at":"2019-01-25T21:18:03Z","abstract_excerpt":"This paper is a survey on the role of Higgs bundle theory in the study of higher Teichm\\\"uller spaces. Recall that the Teichm\\\"uller space of a compact surface can be identified with a certain connected component of the moduli space of representations of the fundamental group of the surface into $\\mathrm{PSL}(2,{\\mathbb{R}})$. Higher Teichm\\\"uller spaces correspond to special components of the moduli space of representations when one replaces $\\mathrm{PSL}(2,{\\mathbb{R}})$ by a real non-compact semisimple Lie group of higher rank. Examples of these spaces are provided by the Hitchin components"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.09086","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"}