{"paper":{"title":"Archipelago groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Gregory R. Conner, Mark Meilstrup, Wolfram Hojka","submitted_at":"2014-10-30T15:00:33Z","abstract_excerpt":"The classical archipelago is a non-contractible subset of $\\mathbb{R}^3$ which is homeomorphic to a disk except at one non-manifold point. Its fundamental group, $\\mathcal{A}$, is the quotient of the topologist's product of $\\mathbb Z$, the fundamental group of the shrinking wedge of countably many copies of the circle (the Hawaiian earring), modulo the corresponding free product. We show $\\mathcal{A}$ is locally free, not indicable, and has the rationals both as a subgroup and a quotient group. Replacing $\\mathbb Z$ with arbitrary groups yields the notion of archipelago groups.\n  Surprisingly"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8389","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"}