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… 
Polynomially bounded cohomology and the Novikov Conjecture
We show that complex group cohomology classes of a countable discrete groupwhich are poly- nomially bounded pair with the topological K-theory of the reduced C � -algebra ofin a way that extends the
Burghelea conjecture and asymptotic dimension of groups
We review the Burghelea conjecture, which constitutes a full computation of the periodic cyclic homology of complex group rings, and its relation to the algebraic Baum–Connes conjecture. The
On properties of relatively hyperbolic groups by Ming
We discuss a number of problems in relatively hyperbolic groups. We show that the word problem and the conjugacy (search) problem are solvable in linear and quadratic time, respectively, for a
Bounded homotopy theory and the K-theory of weighted complexes
Given a bounding class B, we construct a bounded refinement BK(−) of Quillen’s K-theory functor from rings to spaces. As defined, BK(−) is a functor from weighted rings to spaces, and is equipped
Tracing cyclic homology pairings under twisting of graded algebras
We give a description of cyclic cohomology and its pairing with K-groups for 2-cocycle deformation of algebras graded over discrete groups. The proof relies on a realization of monodromy for the
Permute and conjugate: the conjugacy problem in relatively hyperbolic groups
Modelled on efficient algorithms for solving the conjugacy problem in hyperbolic groups, we define and study the permutation conjugacy length (PCL) function. This function estimates the length of a
A spectral sequence for polynomially bounded cohomology
Time complexity of the conjugacy problem in relatively hyperbolic groups
TLDR
It is shown that both the conjugacy problem and the Conjugacy search problem can be solved in polynomial time in a relatively hyperbolic group, whenever the corresponding problem can been solved inPolynomialTime in each parabolic subgroup.
On the Hochschild homology of $\ell^1$-rapid decay group algebras
We show that for many semi-hyperbolic groups the decomposition into conjugacy classes of the Hochschild homology of the l^1-rapid decay group algebra is injective.
...
...

References

SHOWING 1-10 OF 101 REFERENCES
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
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
...
...