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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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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.

References
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Additional Information
  • Laura Ciobanu
  • Affiliation: Department of Mathematics, University of Neuchâtel, Rue Emile Argand 11, CH-2000 Neuchâtel, Switzerland
  • MR Author ID: 797163
  • 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
  • MR Author ID: 219150
  • Email: Sarah.Rees@newcastle.ac.uk
  • Received by editor(s): March 7, 2014
  • Received by editor(s) in revised form: July 31, 2014
  • Published electronically: November 16, 2015
  • © Copyright 2015 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 368 (2016), 6103-6129
  • MSC (2010): Primary 20E06, 43A15, 46L99
  • DOI: https://doi.org/10.1090/tran/6532
  • MathSciNet review: 3461028