{"paper":{"title":"Pictures of KK-theory for real C*-algebras and almost commuting matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Efren Ruiz, Jeffrey L. Boersema, Terry A. Loring","submitted_at":"2012-10-11T06:03:39Z","abstract_excerpt":"We give a systematic account of the various pictures of KK-theory for real C*-algebras, proving natural isomorphisms between the groups that arise from each picture. As part of this project, we develop the universal properties of KK-theory, and we use CRT-structures to prove that a natural transformation from F(A) to G(A) between homotopy equivalent, stable, half-exact functors defined on real C*-algebras is an isomorphism provided it is an isomorphism on the smaller class of C*-algebras. Finally, we develop E-theory for real C*-algebras and use that to obtain new negative results regarding th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3133","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"}