{"paper":{"title":"Non-orientable genus of knots in punctured Spin 4-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Kouki Sato","submitted_at":"2014-11-18T10:59:18Z","abstract_excerpt":"For a closed 4-manifold $X$ and a knot $K$ in the boundary of punctured $X$, we define $\\gamma_X^0(K)$ to be the smallest first Betti number of non-orientable and null-homologous surfaces in punctured $X$ with boundary $K$. Note that $\\gamma^0_{S^4}$ is equal to the non-orientable 4-ball genus and hence $\\gamma^0_X$ is a generalization of the non-orientable 4-ball genus. While it is very likely that for given $X$, $\\gamma^0_X$ has no upper bound, it is difficult to show it. In fact, even in the case of $\\gamma^0_{S^4}$, its non-boundedness was shown for the first time by Batson in 2012. In thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4803","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"}