{"paper":{"title":"On the metastable Mabillard-Wagner conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.GT","authors_text":"A. Skopenkov","submitted_at":"2017-02-14T15:20:23Z","abstract_excerpt":"The purpose of this note is to attract attention to the following conjecture (metastable $r$-fold Whitney trick) by clarifying its status as not having a complete proof, in the sense described in the paper.\n  Assume that $D=D_1\\sqcup\\ldots\\sqcup D_r$ is disjoint union of $r$ disks of dimension $s$, $f:D\\to B^d$ a proper PL map such that $f\\partial D_1\\cap\\ldots\\cap f\\partial D_r=\\emptyset$, $rd\\ge (r+1)s+3$ and $d\\ge s+3$. If the map $$f^r:\\partial(D_1\\times\\ldots\\times D_r)\\to (B^d)^r-\\{(x,x,\\ldots,x)\\in(B^d)^r\\ |\\ x\\in B^d\\}$$ extends to $D_1\\times\\ldots\\times D_r$, then there is a PL map $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04259","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"}