{"paper":{"title":"Dynamics and geometry of character varieties for surface groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"David Chasteen-Boyd, Sara Maloni, Suzanne Schlich","submitted_at":"2026-07-07T16:30:31Z","abstract_excerpt":"The problem of classifying geometric structures on manifolds is very much related to the discussion of the automorphism groups actions on character varieties, which are spaces of equivalence classes of representations. In this chapter we survey some results on this topic, mostly focusing on representations of surface groups (both in the orientable and non-orientable cases) and free groups. An important principle in the study of the dynamics on character varieties $X=X(\\pi_1(S),G)$ for surface groups $\\pi_1(S)$ is the following dichotomy: when the target group $G$ is compact, $X$ has nontrivial"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06473","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.06473/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}