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We derive explicit lower bounds for \\Lambda in dimensions where previous methods failed, namely for (n,k)\\in {(4,1),(5,1),(5,2),(6,3),(9,1),(10,1)}. With methods from surgery theory and bordism theory several gap phenomena for smooth Yamabe invariants can be deduced."},"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":"1204.1197","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-04-05T12:27:14Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"61b1619042a78037cbde1ec6a36abdd8df8b82d2c65083f92695384480be54e6","abstract_canon_sha256":"158863e41b0579cf6627e352ab5cce7fbdfcc711d85fa644683ed629f092b526"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:41.002758Z","signature_b64":"3NBpvh3WDiWwUFd1E0RlbD2ibTuyls2IL7fmzY7uRGzwIL1Y43JOsHvHybMJWU36WuYVtehHG0HxEtqnzfGRDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e43fb6b73a0580d30c26dffb56ed6459a0a3e72dd4103c504f08dba2037e6c9","last_reissued_at":"2026-05-18T02:28:41.002353Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:41.002353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Low-dimensional surgery and the Yamabe invariant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"Bernd Ammann, Emmanuel Humbert, Mattias Dahl","submitted_at":"2012-04-05T12:27:14Z","abstract_excerpt":"Assume that M is a compact n-dimensional manifold and that N is obtained by surgery along a k-dimensional sphere, k\\le n-3. 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