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arXiv · 1108.2262

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

Ronghui Ji·Crichton Ogle·Bobby Ramsey
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Abstract

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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Ronghui Ji, Crichton Ogle, Bobby Ramsey. 2012-01-09. On the Hochschild and cyclic (co)homology of rapid decay group algebras. https://doi.org/10.4171/jncg%2F148

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