{"paper":{"title":"Higher topological complexity of aspherical spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"John Oprea, Michael Farber","submitted_at":"2019-02-26T20:34:39Z","abstract_excerpt":"In this article we study the higher topological complexity ${\\sf TC}_r(X)$ in the case when $X$ is an aspherical space, $X=K(\\pi, 1)$ and $r\\ge 2$. We give a characterisation of ${\\sf TC}_r(K(\\pi, 1))$ in terms of classifying spaces for equivariant Bredon cohomology. Our recent paper \\cite{FGLO}, joint with M. Grant and G. Lupton, treats the special case $r=2$. We also obtain in this paper useful lower bounds for ${\\sf TC}_r(\\pi)$ in terms of cohomological dimension of subgroups of $\\pi\\times\\pi\\times \\dots\\times \\pi$ ($r$ times) with certain properties. As an illustration of the main techniqu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10696","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"}