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By deploying dense subalgebras of ℓ 1 (G) we generalize the Bass conjecture in terms of Connes' cyclic homology theory. In particular, we propose a stronger version of the ℓ 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,… (More)

The property that the polynomial cohomology with coefficients of a finitely generated discrete group is canonically isomor-phic to the group cohomology is called the (weak) isocohomological property for the group. In the case when a group is of type HF ∞ , i.e. that has a classifying space with the homotopy type of a cellular complex with finitely many… (More)

- Ronghui Ji
- 2007

We survey the cyclic cohomology associated with various algebras related to discrete groups. We then discuss the motivation and techniques of the cyclic theory approach to various problems in algebra and analysis.

By deploying dense subalgebras of ℓ 1 (G) we generalize the Bass conjecture in terms of Connes' cyclic homology theory. In particular, we propose a stronger version of the ℓ 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,… (More)

By deploying dense subalgebras of ℓ 1 (G) we generalize the Bass conjecture in terms of Connes' cyclic homology theory. In particular, we propose a stronger version of the ℓ 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,… (More)

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