{"paper":{"title":"On hyperbolic once-punctured-torus bundles III: Comparing two tessellations of the complex plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Makoto Sakuma, Warren Dicks","submitted_at":"2008-11-11T10:43:04Z","abstract_excerpt":"To each once-punctured-torus bundle, $T_\\phi$, over the circle with pseudo-Anosov monodromy $\\phi$, there are associated two tessellations of the complex plane: one, $\\Delta(\\phi)$, is (the projection from $\\infty$ of) the triangulation of a horosphere at $\\infty$ induced by the canonical decomposition into ideal tetrahedra, and the other, $CW(\\phi)$, is a fractal tessellation given by the Cannon-Thurston map of the fiber group switching back and forth between gray and white each time it passes through $\\infty$. In this paper, we study the relation between $\\Delta(\\phi)$ and $CW(\\phi)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.1678","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"}