{"paper":{"title":"Most unexposed taut one-relator presentation 2-complexes are finitely unsplittable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Fredric D. Ancel, Pete Sparks","submitted_at":"2019-07-15T20:40:04Z","abstract_excerpt":"The main result of this article is that among the family of one-relator presentation 2-complexes that might be expected to be finitely unsplittable (not the union of two proper subpolyhedra with finite first homology groups) almost all have this property. Included among these one-relator presentation 2-complexes are all generalized dunce hats. A generalized dunce hat is a 2-dimensional polyhedron created by attaching the boundary of a disk $\\Delta$ to a circle $J$ via a map $f : \\partial\\Delta \\rightarrow J$ with the property that there is a point $v$ in $J$ such that $f^{-1}(\\{v\\})$ is a fini"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.06742","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"}