{"paper":{"title":"A ``stable'' version of the Gromov-Lawson conjecture","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"dg-ga","authors_text":"Jonathan Rosenberg, Stephan Stolz","submitted_at":"1994-07-05T18:30:17Z","abstract_excerpt":"We discuss a conjecture of Gromov and Lawson, later modified by Rosenberg, concerning the existence of metrics of positive scalar curvature. It says that a closed spin manifold $M$ of dimension $n\\ge 5$ has such a metric if and only if the index of a suitable ``Dirac\" operator in $KO_n(C^* (\\pi_1(M)))$, the real $K$-theory of the group $C^*$-algebra of the fundamental group of $M$, vanishes. It is known that the vanishing of the index is necessary for existence of a positive scalar curvature metric on $M$, but this is known to be a sufficient condition only if $\\pi_1(M)$ is the trivial group, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"dg-ga/9407002","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"}