{"paper":{"title":"Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Jes\\'us Gonz\\'alez, Lucile Vandembroucq, Mark Grant","submitted_at":"2016-07-29T15:56:23Z","abstract_excerpt":"Let $X$ be a two-cell complex with attaching map $\\alpha\\colon S^q\\to S^p$, and let $C_X$ be the cofiber of the diagonal inclusion $X\\to X\\times X$. It is shown that the topological complexity (${\\rm TC}$) of $X$ agrees with the Lusternik-Schnirelmann category (${\\rm cat}$) of $C_X$ in the (almost stable) range $q\\leq2p-1$. In addition, the equality ${\\rm TC}(X)={\\rm cat}(C_X)$ is proved in the (strict) metastable range $2p-1<q\\leq3(p-1)$ under fairly mild conditions by making use of the Hopf invariant techniques recently developed by the authors in their study of the sectional category of arb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08858","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"}