{"paper":{"title":"Equivariant maps into Anti-de Sitter space and the symplectic geometry of $\\mathbb H^2\\times \\mathbb H^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Andrea Seppi, Francesco Bonsante","submitted_at":"2017-05-31T15:20:26Z","abstract_excerpt":"Given two Fuchsian representations $\\rho_l$ and $\\rho_r$ of the fundamental group of a closed oriented surface $S$ of genus $\\geq 2$, we study the relation between Lagrangian submanifolds of $M_\\rho=(\\mathbb{H}^2/\\rho_l(\\pi_1(S)))\\times (\\mathbb{H}^2/\\rho_r(\\pi_1(S)))$ and $\\rho$-equivariant embeddings $\\sigma$ of $\\widetilde S$ into Anti-de Sitter space, where $\\rho=(\\rho_l,\\rho_r)$ is the corresponding representation into $\\mathrm{PSL}_2\\mathbb R\\times \\mathrm{PSL}_2\\mathbb R$. It is known that, if $\\sigma$ is a maximal embedding, then its Gauss map takes values in the unique minimal Lagrang"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00846","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"}