271 research outputs found
Relatively hyperbolic groups, rapid decay algebras, and a generalization of the Bass conjecture
By deploying dense subalgebras of we generalize the Bass
conjecture in terms of Connes' cyclic homology theory. In particular, we
propose a stronger version of the -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 -Stronger-Bass Conjecture. Moreover, we determine the
conjugacy-bound for relatively hyperbolic groups and compute the cyclic
cohomology of the -algebra of any discrete group.Comment: 32 pages, 2 figures; added an appendix also by C. Ogl
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