{"paper":{"title":"Cut open null-bordisms and derivatives of slice knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Christopher William Davis, Tim Cochran","submitted_at":"2015-11-23T16:17:20Z","abstract_excerpt":"In the 60's Levine proved that if $R$ is a slice knot, then on any genus $g$ Seifert surface for $R$ there is a $g$ component link $J$, called a derivative of $R$, on which the Seifert form vanishes. Many subsequent obstructions to $R$ being slice are given in terms of slice obstructions of $J$. Many of these obstructions can be derived from a 4-manifold called a null-bordism. Recently the authors proved that that it is possible for $R$ to be slice without $J$ being slice, disproving a conjecture of Kauffmann from the 80's. In this paper we cut open these null-bordisms in order to derive new o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07295","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"}