Genericity of pseudo-Anosov mapping classes, when seen as mapping classes

  • Viveka Erlandsson

    University of Bristol, UK
  • Juan Souto

    Université de Rennes, France
  • Jing Tao

    University of Oklahoma, Norman, USA
Genericity of pseudo-Anosov mapping classes, when seen as mapping classes cover

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Abstract

We prove that pseudo-Anosov mapping classes are generic with respect to certain notions of genericity reflecting that we are dealing with mapping classes. More precisely, we consider a number of functions on the mapping class group, and show that the proportion of pseudo-Anosov mapping classes with -value at most tends to 1 as tends to infinity. The functions we consider include measuring the complexity of mapping classes using quasi-conformal distortion or Lipschitz distortion. We present a uniform approach to this problem using geodesic currents.

Cite this article

Viveka Erlandsson, Juan Souto, Jing Tao, Genericity of pseudo-Anosov mapping classes, when seen as mapping classes. Enseign. Math. 66 (2020), no. 3/4, pp. 419–439

DOI 10.4171/LEM/66-3/4-6