# 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} }

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…

## 22 Citations

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