{"paper":{"title":"Every genus one algebraically slice knot is 1-solvable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Carolyn Otto, Christopher W. Davis, Junghwan Park, Taylor E. Martin","submitted_at":"2016-06-01T21:48:42Z","abstract_excerpt":"Cochran, Orr, and Teichner developed a filtration of the knot concordance group indexed by half integers called the solvable filtration. Its terms are denoted by $\\mathcal{F}_n$. It has been shown that $\\mathcal{F}_n/\\mathcal{F}_{n.5}$ is a very large group for $n\\ge 0$. For a generalization to the setting of links the third author showed that $\\mathcal{F}_{n.5}/\\mathcal{F}_{n+1}$ is non-trivial. In this paper we provide evidence that for knots $\\mathcal{F}_{0.5}=\\mathcal{F}_1$. In particular we prove that every genus 1 algebraically slice knot is 1-solvable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00479","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"}