Rapid decay and Baum-Connes for large type Artin groups
Laura Ciobanu, Derek F. Holt and Sarah Rees
Keywords
rapid decay, Baum-Connes, Artin groups
Status
Published in TAMS 368 (2016) 6103--6129.
Abstract
We prove that many Artin groups of large type satisfy the rapid decay
property, including all those of extra-large type. For many of these,
including all 3-generator groups of extra-large type, a result of
Lafforgue applies to show that the groups satisfy the Baum-Connes
conjecture without coefficients.
Our proof of rapid decay combines elementary analysis with
combinatorial techniques, and relies on properties of geodesic
words in Artin groups of large type that were observed in \cite{HoltRees}
by two of the authors of this current article.\\
\noindent 2000 Mathematics Subject Classification: 20E06, 43A15, 46L99.
\noindent Key words: rapid decay, Artin groups
\
The preprint is available as gzipped
dvi (1 kB),
postscript (1 kB) and
pdf files.
Alternatively, you can request a copy by
e-mailing me.