{"paper":{"title":"Computational complexity of topological invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.AT","authors_text":"Manuel Amann","submitted_at":"2011-12-05T00:00:33Z","abstract_excerpt":"We answer the following question posed by Lechuga: Given a simply-connected space $X$ with both $H_*(X,\\qq)$ and $\\pi_*(X)\\otimes \\qq$ being finite-dimensional, what is the computational complexity of an algorithm computing the cup-length and the rational Lusternik--Schnirelmann category of $X$?\n  Basically, by a reduction from the decision problem whether a given graph is $k$-colourable (for $k\\geq 3$) we show that (even stricter versions of the) problems above are $\\mathbf{NP}$-hard."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0812","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"}