{"paper":{"title":"A symplectic map between hyperbolic and complex Teichm\\\"uller theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.GT"],"primary_cat":"math.DG","authors_text":"Jean-Marc Schlenker, Kirill Krasnov","submitted_at":"2008-05-30T20:36:10Z","abstract_excerpt":"Let $S$ be a closed, orientable surface of genus at least 2. The cotangent bundle of the \"hyperbolic'' Teichm\\\"uller space of $S$ can be identified with the space $\\CP$ of complex projective structures on $S$ through measured laminations, while the cotangent bundle of the \"complex'' Teichm\\\"uller space can be identified with $\\CP$ through the Schwarzian derivative. We prove that the resulting map between the two cotangent spaces, although not smooth, is symplectic. The proof uses a variant of the renormalized volume defined for hyperbolic ends."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.0010","kind":"arxiv","version":2},"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"}