{"paper":{"title":"Pleating coordinates for the Teichm\\\"{u}ller space of a punctured torus","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.GT","authors_text":"Caroline Series, Linda Keen","submitted_at":"1992-01-01T00:00:00Z","abstract_excerpt":"We construct new coordinates for the Teichm\\\"uller space Teich of a punctured torus into $\\bold{R} \\times\\bold{R}^+$. The coordinates depend on the representation of Teich as a space of marked Kleinian groups $G_\\mu$ that depend holomorphically on a parameter $\\mu$ varying in a simply connected domain in $\\bold{C}$. They describe the geometry of the hyperbolic manifold $\\bold{H}^3/G_\\mu$; they reflect exactly the visual patterns one sees in the limit sets of the groups $G_\\mu$; and they are directly computable from the generators of $G_\\mu$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9201263","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"}