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The language of geodesics for Garside groups

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Abstract.

We prove that the language of all geodesics of any Garside group, with respect to the generating set of divisors of the Garside element, forms a regular language. In particular, the braid groups admit generating sets where the associated language of geodesics is regular.

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Authors and Affiliations

  1. Department of Mathematics, Brandeis University, Mail Stop 050, Waltham, MA, 02454

    Ruth Charney

  2. Department of Mathematics, Lafayette College, Easton, PA, 18042

    John Meier

Authors
  1. Ruth Charney
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  2. John Meier
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Correspondence to John Meier.

Additional information

in final form: 28 October 2003

Charney was partially supported by NSF grant DMS-0104026. Meier thanks the AMS for the support of a Centennial Research Fellowship.

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Charney, R., Meier, J. The language of geodesics for Garside groups. Math. Z. 248, 495–509 (2004). https://doi.org/10.1007/s00209-004-0666-8

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  • DOI: https://doi.org/10.1007/s00209-004-0666-8

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