{"paper":{"title":"Groupoid C*-algebras and index theory on manifolds with singularities","license":"","headline":"","cross_cats":["math.OA"],"primary_cat":"math.DG","authors_text":"Jonathan Rosenberg","submitted_at":"2001-05-10T19:40:32Z","abstract_excerpt":"The simplest case of a manifold with singularities is a manifold M with boundary, together with an identification of the boundary with a product M1 x P, where P is a fixed manifold. The associated singular space is obtained by collapsing P to a point. When P = Z/k or S^1, we show how to attach to such a space a noncommutative C*-algebra that captures the extra structure. We then use this C*-algebra to give a new proof of the Freed-Melrose Z/k-index theorem and a proof of an index theorem for manifolds with S^1 singularities. Our proofs apply to the real as well as to the complex case. Applicat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0105085","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"}