{"paper":{"title":"A hierarchy for closed n-cell-complements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Robert J. Daverman, Shijie Gu","submitted_at":"2014-11-10T22:48:39Z","abstract_excerpt":"Let $C$ and $D$ be a pair of crumpled $n$-cubes and $h$ a homeomorphism of $\\text{Bd }C$ to $\\text{Bd }D$ for which there exists a map $f_h: C\\to D$ such that $f_h|\\text{Bd }C =h$ and $f_{h}^{-1}(\\text{Bd }D)=\\text{Bd }C$. In our view the presence of such a triple $(C,D,h)$ suggests that $C$ is \"at least as wild as\" $D$. The collection $\\mathscr{W}_n$ of all such triples is the subject of this paper. If $(C,D,h)\\in \\mathscr{W}_n$ but there is no homeomorphism such that $D$ is at least as wild as $C$, we say $C$ is \"strictly wilder than\" $D$. The latter concept imposes a partial order on the co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2652","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"}