{"paper":{"title":"Splittings of link concordance groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Carolyn Otto, Taylor E. Martin","submitted_at":"2016-06-01T22:03:44Z","abstract_excerpt":"We establish several results about two short exact sequences involving lower terms of the $n$-solvable filtration, $\\{\\mathcal{F}^m_n\\}$ of the string link concordance group $\\mathcal{C}^m$. We utilize the Thom-Pontryagin construction to show that the Sato-Levine invariants $\\bar{\\mu}_{(iijj)}$ must vanish for 0.5-solvable links. Using this result, we show that the short exact sequence $0\\rightarrow \\mathcal{F}^m_0/\\mathcal{F}^m_{0.5} \\rightarrow \\mathcal{F}^m_{-0.5}/\\mathcal{F}^m_{0.5} \\rightarrow \\mathcal{F}^m_{-0.5}/\\mathcal{F}^m_0 \\rightarrow 0$ does not split for links of two or more comp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00481","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"}