{"paper":{"title":"Rho-classes, index theory and Stolz' positive scalar curvature sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GT"],"primary_cat":"math.KT","authors_text":"Paolo Piazza (Universita La Sapienza Roma), Thomas Schick (Georg-August-Universit\\\"at G\\\"ottingen)","submitted_at":"2012-10-25T16:18:32Z","abstract_excerpt":"In this paper, we study the space of metrics of positive scalar curvature using methods from coarse geometry.\n  Given a closed spin manifold M with fundamental group G, Stephan Stolz introduced the positive scalar curvature exact sequence, in analogy to the surgery exact sequence in topology. It calculates a structure group of metrics of positive scalar curvature on M (the object we want to understand) in terms of spin-bordism of BG and a somewhat mysterious group R(G).\n  Higson and Roe introduced a K-theory exact sequence in coarse geometry which contains the Baum-Connes assembly map, with on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6892","kind":"arxiv","version":3},"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"}