{"paper":{"title":"Trace class operators, regulators, and assembly maps in K-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Gisela Tartaglia, Guillermo Corti\\~nas","submitted_at":"2013-05-08T10:44:11Z","abstract_excerpt":"Let G be a group, Fin the family of its finite subgroups, and E(G,Fin) the classifying space. Let L^1 be the algebra of trace-class operators in an infinite dimensional, separable Hilbert space over the complex numbers. Consider the rational assembly map in homotopy algebraic K-theory H_p^G(E(G,Fin),KH(L^1))\\otimes\\Q \\to KH_p(L^1[G])\\otimes\\Q. The rational KH-isomorphism conjecture predicts that the map above is an isomorphism; it follows from a theorem of Yu (see arXiv:1106.3796, arXiv:1202.4999) that it is always injective. In the current article we prove the following. Theorem: Assume that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1771","kind":"arxiv","version":2},"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"}