{"paper":{"title":"Projective product coverings and sequential motion planning algorithms in real projective spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Adriana Lara, Darwin Gutierrez, Jesus Gonzalez","submitted_at":"2016-05-25T17:03:37Z","abstract_excerpt":"For positive integers $m$ and $s$, let $\\mathbf{m}_s$ stand for the $s$-th tuple $(m,\\ldots,m)$. We show that, for large enough $s$, the higher topological complexity $TC_s$ of an even dimensional real projective space $RP^m$ is characterized as the smallest positive integer $k=k(m,s)$ for which there is a $(\\mathbb{Z}_2)^{s-1}$-equivariant map from Davis' projective product space $P_{\\mathbf{m}_s}$ to the $(k+1)$-th join-power $((\\mathbb{Z}_2)^{s-1})^{\\ast(k+1)}$. This is a (partial) generalization of Farber-Tabachnikov-Yuzvinsky's work relating $TC_2$ to the immersion dimension of real proje"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07966","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"}