{"paper":{"title":"Ascent sliceness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"William Rushworth","submitted_at":"2018-02-05T23:16:20Z","abstract_excerpt":"We introduce the notion of ascent sliceness of virtual knots. A representative of a virtual knot is an embedding $ S^1 \\hookrightarrow \\Sigma_{g} \\times I $, for $ \\Sigma_g $ a closed connected oriented surface of genus $ g $; the virtual knot represented is slice if there exists a pair consisting of a disc $ D $ and an oriented $ 3 $-manifold $ M $, such that $ D \\hookrightarrow M \\times I $, $ \\partial M = \\Sigma_{g} $, and $ \\partial D = S^1 $ (the image of the embedding).\n  This definition of sliceness exemplifies that a cobordism of virtual links is a pair consisting of a surface and a $ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01727","kind":"arxiv","version":3},"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"}