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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References

SHOWING 1-10 OF 101 REFERENCES
Smooth dense subalgebras of reduced group C∗-algebras, Schwartz cohomology of groups, and cyclic cohomology
On a class of groups satisfying Bass' conjecture
Abstract. In this paper, we use the Connes-Karoubi character liftings of the Hattori-Stallings rank in order to obtain examples of groups satisfying Bass' conjecture. We consider the nilpotence of…
Spaces over a category and assembly maps in isomorphism conjectures in K- and L-theory.
We give a unified approach to the Isomorphism Conjecture of Farrell and Jones on the algebraic K- and L-theory of integral group rings and to the Baum-Connes Conjecture on the topological K-theory of…
The conjugacy problem for relatively hyperbolic groups
Solvability of the conjugacy problem for relatively hyperbolic groups was announced by Gromov (18). Using the definition of Farb of a relatively hyperbolic group in the strong sense (14), we prove…
Groups acting on tree-graded spaces and splittings of relatively hyperbolic groups☆
THE BAUM-CONNES ASSEMBLY MAP AND THE GENERALIZED BASS CONJECTURE
We show that the image of Connes-Karoubi-Chern character, restricted to the image of the Baum-Connes assembly map in the Bott-periodized topological K-theory of the complex group algebra, lies in the…
Relatively hyperbolic Groups
TLDR
This paper defines the boundary of a relatively hyperbolic group, and shows that the limit set of any geometrically finite action of the group is equivariantly homeomorphic to this boundary, and generalizes a result of Tukia for geometRically finite kleinian groups.
E-theory and KK-theory for groups which act properly and isometrically on Hilbert space
A good deal of research in C∗-algebra K -theory in recent years has been devoted to the Baum-Connes conjecture [3], which proposes a formula for the K -theory of group C∗-algebras that blends group…
CHERN CHARACTER FOR DISCRETE GROUPS
Polynomially bounded cohomology and discrete groups
...
...