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… 
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