On the Hochschild and cyclic (co)homology of rapid decay group algebras

Details On the Hochschild and cyclic (co)homology of rapid decay group algebras On the Hochschild and cyclic (co)homology of rapid decay group algebras

2011-08-10

arxiv.org/abs/1108.2262v3

Mathematics

K-Theory and Homology

Scientific paper

We show that the technical condition of solvable conjugacy bound, introduced in \cite{JOR1}, can be removed without affecting the main results of that paper. The result is a Burghelea-type description of the summands $HH_*^t(\BG)_{}$ and $HC_*^t(\BG)_{}$ for any bounding class $\B$, discrete group with word-length $(G,L)$ and conjugacy class $\in $. We use this description to prove the conjecture $\B$-SrBC of \cite{JOR1} for a class of groups that goes well beyond the cases considered in that paper. In particular, we show that the conjecture $\ell^1$-SrBC (the Strong Bass Conjecture for the topological $K$-theory of $\ell^1(G)$) is true for all semihyperbolic groups which satisfy SrBC, a statement consistent with the rationalized Bost conjecture for such groups.

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