{"paper":{"title":"Cochran's $\\beta^i$ invariants via twisted Whitney towers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Jim Conant, Peter Teichner, Rob Schneiderman","submitted_at":"2016-07-06T17:42:08Z","abstract_excerpt":"We show that Tim Cochran's invariants $\\beta^i(L)$ of a $2$-component link $L$ in the $3$--sphere can be computed as intersection invariants of certain 2-complexes in the $4$--ball with boundary $L$. These 2-complexes are special types of twisted Whitney towers, which we call {\\em Cochran towers}, and which exhibit a new phenomenon: A Cochran tower of order $2k$ allows the computation of the $\\beta^i$ invariants for all $i\\leq k$, i.e. simultaneous extraction of invariants from a Whitney tower at multiple orders. This is in contrast with the order $n$ Milnor invariants (requiring order $n$ Whi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01722","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"}