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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1607.08858","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-07-29T15:56:23Z","cross_cats_sorted":[],"title_canon_sha256":"861d689c9c0e847c540d7d37abff55446c478d1d8f901ef3ef5e36502cd07a0f","abstract_canon_sha256":"4c39e2636a5daf99edf5779e363d2789e14c2e44f3d73cbe519d8a43f5e0392b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:15.734886Z","signature_b64":"uZv9JwuI/oGnihP+C2DHhDmtGvXwBulzPCsGvUQ1yf4HH96RFU25l3FDS3GcqEZ1kz59K8fPg0C0Pg3i6WirBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4204ed9c2d0b49a82f435b8241c1bdd46bfd0e359bded5fbfb2483ec46762b56","last_reissued_at":"2026-05-18T01:10:15.734171Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:15.734171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $X\\to X\\times X$. 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