{"paper":{"title":"A Note on Kasparov Product and Duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.OA","authors_text":"Hyun Ho Lee","submitted_at":"2007-12-11T22:53:13Z","abstract_excerpt":"Using Paschke-Higson duality, we can get a natural index pairing $K_{i}(A) \\times K_{i+1}(D_{\\Phi}) \\to \\boldsymbol{Z} \\quad (i=0,1) (\\mbox{mod}2)$, where $A$ is a separable $C\\sp*$-algebra, and $\\Phi$ is a representation of $A$ on a separable infinite dimensional Hilbert space $H$. It is proved that this is a special case of the Kasparov Product. As a step, we show a proof of Bott-periodicity for KK-theory asserting that $\\mathbb{C}_1$ and $S$ are $KK$-equivalent using the odd index pairing."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.1842","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"}