{"paper":{"title":"Smoothly embedding Seifert fibered spaces in $S^4$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ahmad Issa, Duncan McCoy","submitted_at":"2018-10-10T23:02:11Z","abstract_excerpt":"Using an obstruction based on Donaldson's theorem, we derive strong restrictions on when a Seifert fibered space $Y = F(e; \\frac{p_1}{q_1}, \\ldots, \\frac{p_k}{q_k})$ over an orientable base surface $F$ can smoothly embed in $S^4$. This allows us to classify precisely when $Y$ smoothly embeds provided $e > k/2$, where $e$ is the normalized central weight and $k$ is the number of singular fibers. Based on these results and an analysis of the Neumann-Siebenmann invariant $\\overline{\\mu}$, we make some conjectures concerning Seifert fibered spaces which embed in $S^4$. Finally, we also provide som"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04770","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"}