{"paper":{"title":"New lower bounds for the topological complexity of aspherical spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Gregory Lupton, John Oprea, Mark Grant","submitted_at":"2013-09-17T06:12:26Z","abstract_excerpt":"We show that the topological complexity of an aspherical space $X$ is bounded below by the cohomological dimension of the direct product $A\\times B$, whenever $A$ and $B$ are subgroups of $\\pi_1(X)$ whose conjugates intersect trivially. For instance, this assumption is satisfied whenever $A$ and $B$ are complementary subgroups of $\\pi_1(X)$. This gives computable lower bounds for the topological complexity of many groups of interest (including semidirect products, pure braid groups, certain link groups, and Higman's acyclic four-generator group), which in some cases improve upon the standard l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4192","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"}