# Relatively hyperbolic groups, rapid decay algebras and a generalization of the Bass conjecture

@article{Ji2010RelativelyHG,
title={Relatively hyperbolic groups, rapid decay algebras and a generalization of the Bass conjecture},
author={Ran Ji and Crichton Ogle and Bobby Ramsey},
journal={Journal of Noncommutative Geometry},
year={2010},
volume={4},
pages={83-124}
}
• Published 25 July 2007
• Mathematics
• Journal of Noncommutative Geometry
By deploying dense subalgebras of  1 .G/ we generalize the Bass conjecture in terms of Connes' cyclic homology theory. In particular, we propose a stronger version of the  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 ` 1 -Stronger-Bass Conjecture. Moreover, we determine the conjugacy bound for relatively hyperbolic groups and compute the…
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