{"paper":{"title":"Heegaard structure respects complicated JSJ decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"David Bachman, Eric Sedgwick, Ryan Derby-Talbot","submitted_at":"2009-11-27T20:53:57Z","abstract_excerpt":"Let $M$ be a 3-manifold with torus boundary components $T_1$ and $T_2$. Let $\\phi \\colon T_1 \\to T_2$ be a homeomorphism, $M_\\phi$ the manifold obtained from $M$ by gluing $T_1$ to $T_2$ via the map $\\phi$, and $T$ the image of $T_1$ in $M_\\phi$. We show that if $\\phi$ is \"sufficiently complicated\" then any incompressible or strongly irreducible surface in $M_\\phi$ can be isotoped to be disjoint from $T$. It follows that every Heegaard splitting of a 3-manifold admitting a \"sufficiently complicated\" JSJ decomposition is an amalgamation of Heegaard splittings of the components of the JSJ decomp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.5078","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"}