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Rapid decay and Baum-Connes for large type Artin groups


Authors: Laura Ciobanu, Derek F. Holt and Sarah Rees
Journal: Trans. Amer. Math. Soc. 368 (2016), 6103-6129
MSC (2010): Primary 20E06, 43A15, 46L99
DOI: https://doi.org/10.1090/tran/6532
Published electronically: November 16, 2015
MathSciNet review: 3461028
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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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Additional Information

Laura Ciobanu
Affiliation: Department of Mathematics, University of Neuchâtel, Rue Emile Argand 11, CH-2000 Neuchâtel, Switzerland
Email: Laura.Ciobanu@unine.ch

Derek F. Holt
Affiliation: Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
Email: D.F.Holt@warwick.ac.uk

Sarah Rees
Affiliation: School of Mathematics and Statistics, University of Newcastle, Newcastle, NE1 7RU, United Kingdom
Email: Sarah.Rees@newcastle.ac.uk

DOI: https://doi.org/10.1090/tran/6532
Keywords: Rapid decay, Artin groups
Received by editor(s): March 7, 2014
Received by editor(s) in revised form: July 31, 2014
Published electronically: November 16, 2015
Article copyright: © Copyright 2015 American Mathematical Society