{"paper":{"title":"Extension of incompressible surfaces on the boundary of 3-manifolds","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Hugh Howards, Michael Freedman, Ying-Qing Wu","submitted_at":"1997-06-30T00:00:00Z","abstract_excerpt":"An incompressible surface $F$ on the boundary of a compact orientable 3-manifold $M$ is arc-extendible if there is an arc $\\gamma$ on $\\partial M - $ Int $F$ such that $F \\cup N(\\gamma)$ is incompressible, where $N(\\gamma)$ is a regular neighborhood of $\\gamma$ in $\\partial M$. Suppose for simplicity that $M$ is irreducible, and $F$ has no disk components. If $M$ is a product $F\\times I$, or if $\\partial M - F$ is a set of annuli, then clearly $F$ is not arc-extendible. The main theorem of this paper shows that these are the only obstructions for $F$ to be arc-extendible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9706222","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"}