{"paper":{"title":"A K-Theory Proof of the Cobordism Invariance of the Index","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.KT","authors_text":"Catarina Carvalho","submitted_at":"2004-08-19T12:24:17Z","abstract_excerpt":"We give a proof of the cobordism invariance of the index of elliptic pseudodifferential operators on sigma-compact manifolds, where, in the non-compact case, the operators are assumed to be multiplication outside a compact set. We show that, if the principal symbol class of such an elliptic operator on the boundary of a manifold X has a suitable extension to K^1(TX), then its index is zero. This condition is incorporated into the definition of a cobordism group for non-compact manifolds, called here ``cobordism of symbols''.\n Our proof is topological, in that we use properties of the push-forw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0408260","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"}