Relatively hyperbolic groups, rapid decay algebras, and a generalization of the Bass conjecture
Abstract
By deploying dense subalgebras of $\ell^1(G)$ we generalize the Bass conjecture in terms of Connes' cyclic homology theory. In particular, we propose a stronger version of the $\ell^1$-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 $\ell^1$-Stronger-Bass Conjecture. Moreover, we determine the conjugacy-bound for relatively hyperbolic groups and compute the cyclic cohomology of the $\ell^1$-algebra of any discrete group.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2007
- DOI:
- 10.48550/arXiv.0707.3658
- arXiv:
- arXiv:0707.3658
- Bibcode:
- 2007arXiv0707.3658J
- Keywords:
-
- Mathematics - K-Theory and Homology;
- 46L80
- E-Print:
- 32 pages, 2 figures