{"paper":{"title":"Cannon-Thurston fibers for iwip automorphisms of $F_N$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Ilya Kapovich, Martin Lustig","submitted_at":"2012-07-15T11:29:32Z","abstract_excerpt":"For any atoroidal iwip $\\phi \\in Out(F_N)$ the mapping torus group $G_\\phi=F_N\\rtimes_\\phi <t>e$ is hyperbolic, and the embedding $\\iota: F_N \\overset{\\lhd}{\\longrightarrow} G_\\phi$ induces a continuous, $F_N$-equivariant and surjective {\\em Cannon-Thurston map} $\\hat \\iota: \\partial F_N \\to \\partial G_\\phi$.\n  We prove that for any $\\phi$ as above, the map $\\hat \\iota$ is finite-to-one and that the preimage of every point of $\\partial G_\\phi$ has cardinality $\\le 2N$.\n  We also prove that every point $S\\in \\partial G_\\phi$ with $\\ge 3$ preimages in $\\partial F_N$ has the form $(wt^m)^\\infty$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3494","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"}