{"paper":{"title":"A concordance analogue of the $4$-dimensional light bulb theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Maggie Miller","submitted_at":"2019-03-07T17:24:04Z","abstract_excerpt":"We prove a concordance analogue of Gabai's $4$-dimensional light bulb theorem. That is, we show that when $R$ and $R'$ are homotopically (smoothly) embedded $2$-spheres in a $4$-manifold $X^4$ where $\\pi_1(X^4)$ has no $2$-torsion and one of $R$ or $R'$ has a transverse sphere, then $R$ and $R'$ are concordant. When $\\pi_1(X^4)$ has $2$-torsion, we give a similar statement with extra hypotheses as in the $4$-dimensional light bulb theorem. We also give similar statements when $R$ and $R'$ are orientable positive-genus surfaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.03055","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"}