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We prove this for groups G with low-dimensional classifying space, provided the assembly map for G is injective.\n  On the other hand, we construct a spin manifold with no metric with scal>0 but so that already its KO-orientation in KO_*(B pi_1(M)) vanishes. Therefore a corresponding weakened version or the GLR-conjecture is wrong.\n  Last we address non-orientable ma"},"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":"math/9903007","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"1999-03-01T17:03:11Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"35434d5833176921009c3d1a618605912c3fa29629e6bd9f4dea41b0c27cd4e2","abstract_canon_sha256":"7a7d2754a3d312f091fbb300ec9bc91e4ece7f5c5cd1925c63a2379362c76e71"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:44.805895Z","signature_b64":"IrfyWUnV5ddO5YzJoJe5jPzYtDlCsqYMVOHkvWkP/AeH53htbJOI7WuVORTnVMGgceOtaBNbPqA0S90XRdJHBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42ca2b8b4ed10fc94bcf6419ef27d61f190d59e974b5b5d11d2d324988ae24f4","last_reissued_at":"2026-05-17T23:59:44.805518Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:44.805518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Positive and negative results concerning the Gromov-Lawson-Rosenberg conjecture","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Michael Joachim, Thomas Schick","submitted_at":"1999-03-01T17:03:11Z","abstract_excerpt":"The Gromov-Lawson-Rosenberg-conjecture for a group G states that a closed spin manifold M^n (n>4) with fundamental group G admits a metric with positive scalar curvature if and only if its C^*-index A(M) in KO_n(C^*_r(G)) vanishes. 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