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Let $C_1(X)$ denote the 1-dimensional cobordism category and let $Circ(X) \\subset C_1(X)$ denote the subcategory whose objects are disjoint unions of unparametrised circles in $\\mathbb{R}^\\infty$. Multiplication in $S^1$ induces a functor $Circ(X) \\to Circ(LX)$, and the composition of this functor with the inclusion of $Circ(LX)$ into $C_1(LX)$ is homo"},"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":"1711.09433","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-11-26T18:03:17Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"ae833288efc2878264ee7045d3c5392d0d99c204740d54bbcb32c725b1b02893","abstract_canon_sha256":"5f8df1d48f10b8b12c48e5a2ede54fcc193f571f5d46aee13177a972cdbc1614"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:13.395522Z","signature_b64":"m95ZK7gghX28AT7a5JFrMTLIW9uwMD2LvlQxNp6vydoRoBZ3EihlmVa8ptLc7fHevsAcoYJDChjSjqg3CaxZBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6d81d5cd0c6632bdd946ed608cbb908230feab4321484983f0e9e566573d4bb","last_reissued_at":"2026-05-17T23:41:13.395012Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:13.395012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The circle transfer and cobordism categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Jeffrey Giansiracusa","submitted_at":"2017-11-26T18:03:17Z","abstract_excerpt":"The circle transfer $Q\\Sigma (LX_{hS^1})_+ \\to QLX_+$ has appeared in several contexts in topology. 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