Rapid decay and Baum-Connes for large type Artin groups

Ciobanu, Laura; Holt, Derek; Rees, Sarah

doi:10.1090/tran/6532

Rapid decay and Baum-Connes for large type Artin groups
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by Laura Ciobanu, Derek F. Holt and Sarah Rees PDF

Trans. Amer. Math. Soc. 368 (2016), 6103-6129 Request permission

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 earlier work by two of the authors of this current article.

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