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On the minimum dilatation of braids on punctured discs

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Abstract

We find the minimum dilatation of pseudo-Anosov braids on n-punctured discs for 3 ≤ n ≤ 8. This covers the results of Song-Ko-Los (n = 4) and Ham-Song (n = 5). The proof is elementary, and uses the Lefschetz formula.

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Authors and Affiliations

  1. Centre de Physique Théorique (CPT), UMR CNRS 6207, Université du Sud Toulon-Var and Fédération de Recherches des Unités de Mathématiques de Marseille, Luminy, Case 907, 13288, Marseille Cedex 9, France

    Erwan Lanneau

  2. Department of Mathematics, University of Wisconsin, Van Vleck Hall, 480 Lincoln Drive, Madison, WI, 53706, USA

    Jean-Luc Thiffeault

Authors
  1. Erwan Lanneau
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  2. Jean-Luc Thiffeault
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Correspondence to Erwan Lanneau.

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Lanneau, E., Thiffeault, JL. On the minimum dilatation of braids on punctured discs. Geom Dedicata 152, 165–182 (2011). https://doi.org/10.1007/s10711-010-9551-2

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