Rapid decay and Baum-Connes for large type Artin groups

Laura Ciobanu, Derek F. Holt and Sarah Rees


rapid decay, Baum-Connes, Artin groups


to appear in TAMS


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 \

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