{"paper":{"title":"Equivariant K-theory and the Chern character for discrete groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.KT","authors_text":"Efton Park","submitted_at":"2010-10-29T16:51:19Z","abstract_excerpt":"Let $X$ be a compact Hausdorff space, let $\\Gamma$ be a discrete group that acts continuously on $X$ from the right, define $\\widetilde{X} = \\{(x,\\gamma) \\in X \\times \\Gamma : x\\cdot\\gamma= x\\}$, and let $\\Gamma$ act on $\\widetilde{X}$ via the formula $(x,\\gamma)\\cdot\\alpha = (x\\cdot\\alpha, \\alpha^{-1}\\gamma\\alpha)$. Results of P. Baum and A. Connes, along with facts about the Chern character, imply that $K^i_\\Gamma(X) \\otimes \\mathbb{C} \\cong K^i(\\widetilde{X}\\slash\\Gamma) \\otimes \\mathbb{C}$ for $i = 0, -1$. In this note, we present an example where the groups $K^i_\\Gamma(X)$ and $K^i(\\widet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.6271","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"}