{"paper":{"title":"The flux homomorphism on closed hyperbolic surfaces and Anti-de Sitter three-dimensional geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Andrea Seppi","submitted_at":"2017-12-06T21:17:59Z","abstract_excerpt":"Given a smooth spacelike surface $\\Sigma$ of negative curvature in Anti-de Sitter space of dimension 3, invariant by a representation $\\rho:\\pi_1(S)\\to\\mathrm{PSL}_2\\mathbb{R}\\times\\mathrm{PSL}_2\\mathbb{R}$ where $S$ is a closed oriented surface of genus $\\geq 2$, a canonical construction associates to $\\Sigma$ a diffeomorphism $\\phi_\\Sigma$ of $S$. It turns out that $\\phi_\\Sigma$ is a symplectomorphism for the area forms of the two hyperbolic metrics $h$ and $h'$ on $S$ induced by the action of $\\rho$ on $\\mathbb{H}^2\\times\\mathbb{H}^2$. Using an algebraic construction related to the flux hom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02413","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"}