{"paper":{"title":"Relatively hyperbolic groups, rapid decay algebras, and a generalization of the Bass conjecture","license":"","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"B. Ramsey, C. Ogle, R. Ji","submitted_at":"2007-07-25T01:43:34Z","abstract_excerpt":"By deploying dense subalgebras of $\\ell^1(G)$ we generalize the Bass conjecture in terms of Connes' cyclic homology theory. In particular, we propose a stronger version of the $\\ell^1$-Bass Conjecture. We prove that hyperbolic groups relative to finitely many subgroups, each of which posses the polynomial conjugacy-bound property and nilpotent periodicity property, satisfy the $\\ell^1$-Stronger-Bass Conjecture. Moreover, we determine the conjugacy-bound for relatively hyperbolic groups and compute the cyclic cohomology of the $\\ell^1$-algebra of any discrete group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.3658","kind":"arxiv","version":3},"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"}